# Herbert W. HamberUniversity of California, Irvine | UCI · Department of Physics and Astronomy

Herbert W. Hamber

Ph.D.

## About

135

Publications

9,275

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3,614

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Introduction

Current research interests include Quantum Chromodynamics (QCD), Quantum Gravitation, Euclidean and Statistical Field Theory, Quantum Cosmology, Non-Perturbative Methods, Computational Physics, Large Scale Computation.

Additional affiliations

October 2012 - February 2013

August 2011 - September 2011

June 2008 - August 2008

## Publications

Publications (135)

In some models of electro-weak interactions the W and Z bosons are considered
composites, made up of spin-one-half subconstituents. In these models a spin
zero counterpart of the W and Z boson naturally appears, whose higher mass can
be attributed to a particular type of hyperfine spin interaction among the
various subconstituents. Recently it has...

We present a discrete form of the Wheeler-DeWitt equation for quantum
gravitation, based on the lattice formulation due to Regge. In this setup the
infinite-dimensional manifold of 3-geometries is replaced by a space of
three-dimensional piecewise linear spaces, with the solutions to the lattice
equations providing a suitable approximation to the c...

https://www.youtube.com/playlist?list=PLqOZ6FD_RQ7ln1ZQPEU9aZQsEj0eyGlT6
http://ocw.uci.edu/courses/einsteins_general_relativity_and_gravitation.html
Video lectures direct link :
https://www.youtube.com/watch?v=ooPIRrd7RDE
or here : http://www.infocobuild.com/education/audio-video-courses/physics/Physics255-Spring2014-UCI/lecture-01.html

In quantum gravity perturbation theory, Newton’s constant G is known to be badly divergent, and as a result not very useful. Nevertheless, some of the most interesting phenomena in physics are often associated with non-analytic behavior in the coupling constant and the existence of nontrivial quantum condensates. It is therefore possible that patho...

The book covers the theory of Quantum Gravitation from the point of view of Feynman path integrals. These provide a manifestly covariant approach in which fundamental quantum aspects of the theory such as radiative corrections and the renormalization group can be systematically and consistently addressed. The path integral method is suitable for bo...

Unlike scalar and gauge field theories in four dimensions, gravity is not perturbatively renormalizable and as a result perturbation theory is badly divergent. Often the method of choice for investigating nonperturbative effects has been the lattice formulation, and in the case of gravity the Regge–Wheeler lattice path integral lends itself well fo...

Unlike scalar and gauge field theories in four dimensions, gravity is not perturbatively renormalizable and as a result perturbation theory is badly divergent. Often the method of choice for investigating nonperturbative effects has been the lattice formulation, and in the case of gravity the Regge-Wheeler lattice path integral lends itself well fo...

Power spectra play an important role in the theory of inflation, and their ability to reproduce current observational data to high accuracy is often considered a triumph of inflation, largely because of a lack of credible alternatives. In previous work we introduced an alternative picture for the cosmological power spectra based on the nonperturbat...

Power spectra play an important role in the theory of inflation, and their ability to reproduce current observational data to high accuracy is often considered a triumph of inflation, largely because of a lack of credible alternatives. In previous work we introduced an alternative picture for the cosmological power spectra based on the nonperturbat...

Power spectra always play an important role in the theory of inflation. In particular, the ability to reproduce the galaxy matter power spectrum P ( k ) and the CMB temperature angular power spectrum C l ’s to high accuracy is often considered a triumph of inflation. In our previous work, we presented an alternative explanation for the matter power...

Power spectra always play an important role in the theory of inflation. In particular, the ability to reproduce the galaxy matter power spectrum and the CMB temperature angular power spectrum coefficients to high accuracy is often considered a triumph of inflation. In our previous work, we presented an alternative explanation for the matter power s...

Power spectra always play an important role in the theory of inflation. In particular, the ability to reproduce the galaxy matter power spectrum $ P(k) $ and the CMB temperature angular power spectrum $ C_l $’s to high accuracy is often considered a triumph of inflation. In our previous work, we presented an alternative explanation for the matter p...

Power spectra always play an important role in the theory of inflation. In particular, the ability to reproduce the galaxy matter power spectrum P (k) and the CMB temperature angular power spectrum C l 's to high accuracy is often considered a triumph of inflation. In our previous work, we presented an alternative explanation for the matter power s...

The ability to reproduce the observed matter power spectrum P ( k ) to high accuracy is often considered as a triumph of inflation. In this work, we explore an alternative explanation for the power spectrum based on nonperturbative quantum field-theoretical methods applied to Einstein’s gravity, instead of ones based on inflation models. In particu...

In quantum gravity perturbation theory in Newton's constant $G$ is known to be badly divergent, and as a result not very useful. Nevertheless, some of the most interesting phenomena in physics are often associated with non-analytic behavior in the coupling constant and the existence of nontrivial quantum condensates. It is therefore possible that p...

The ability to reproduce the observed matter power spectrum $P(k)$ to high accuracy is often considered as a triumph of inflation.
In this work, we explore an alternative explanation for the power spectrum based on nonperturbative quantum field-theoretical methods applied to Einstein’s gravity, instead of ones based on inflation models.
In particu...

In quantum gravity perturbation theory in Newton's constant G is known to be badly divergent, and as a result not very useful. Nevertheless some of the most interesting phenomena in physics are often associated with non-analytic behavior in the coupling constant and the existence of nontrivial quantum condensates. It is therefore possible that path...

In this work nonperturbative aspects of quantum gravity are investigated using the lattice formulation, and some new results are presented for critical exponents, amplitudes, and invariant correlation functions. Values for the universal scaling dimensions are compared with other nonperturbative approaches to gravity in four dimensions, and specific...

In this work nonperturbative aspects of quantum gravity are investigated using the lattice formulation, and some new results are presented for critical exponents, amplitudes and invariant correlation functions. Values for the universal scaling dimensions are compared with other nonper-turbative approaches to gravity in four dimensions, and specific...

In this work nonperturbative aspects of quantum gravity are investigated using the lattice formulation, and some new results are presented for critical exponents, amplitudes and invariant correlation functions. Values for the universal scaling dimensions are compared with other nonperturbative approaches to gravity in four dimensions, and specifica...

We explore the possible cosmological consequences of a running Newton's constant, G(box), as suggested by the non-trivial ultraviolet fixed point scenario for Einstein gravity with a cosmological constant term. Here, we examine what possible effects a scale-dependent coupling might have on large-scale cosmological density perturbations. Starting fr...

Physical properties of the quantum gravitational vacuum state are explored by
solving a lattice version of the Wheeler-DeWitt equation. The constraint of
diffeomorphism invariance is strong enough to uniquely determine the structure
of the vacuum wave functional in the limit of infinitely fine triangulations of
the three-sphere. In the large fluctu...

We examine the general issue of whether a scale dependent cosmological
constant can be consistent with general covariance, a problem that arises
naturally in the treatment of quantum gravitation where coupling constants
generally run as a consequence of renormalization group effects. The issue is
approached from several points of view, which includ...

The infrared structure of quantum gravity is explored by solving a lattice version of the Wheeler-DeWitt equations. In the present paper only the case of 2 þ 1 dimensions is considered. The nature of the wave function solutions is such that a finite correlation length emerges and naturally cuts off any infrared divergences. Properties of the lattic...

The infrared structure of quantum gravity is explored by solving a lattice version of the Wheeler-DeWitt equations. In the present paper only the case of 2+1 dimensions is considered. The nature of the wave function solutions is such that a finite correlation length emerges and naturally cuts off any infrared divergences. Properties of the lattice...

In some models of electro-weak interactions the W and Z bosons are considered composites,
made up of spin-one-half subconstituents. In these models a spin zero counterpart of the W and Z
boson naturally appears, whose higher mass can be attributed to a particular type of hyperfine spin
interaction among the various subconstituents. Recently it has...

In classical gravity, deviations from the predictions of the Einstein theory are often discussed within the framework of the conformal Newtonian gauge, where scalar perturbations are described by two potentials ϕ and ψ. In this paper we use the above gauge to explore possible cosmological consequences of a running Newton’s constant G(□), as suggest...

We explore possible cosmological consequences of a running Newton’s constant G(□), as suggested by the nontrivial ultraviolet fixed point scenario in the quantum field-theoretic treatment of Einstein gravity with a cosmological constant term. In particular, we focus here on what possible effects the scale-dependent coupling might have on large scal...

We explore possible cosmological consequences of a running Newton's constant G(✷), as suggested by the non-trivial ultraviolet fixed point scenario for Einstein gravity with a cosmological constant term. Here we examine what possible effects a scale-dependent coupling might have on large scale cosmological density perturbations. Starting from a set...

I review the field-theoretic renomalization group approach to quantum gravity, built around the existence of a non-trivial ultraviolet fixed point in four dimensions. I discuss the implications of such a fixed point, found in three largely unrelated non-perturbative approaches, and how it relates to the vacuum state of quantum gravity, and specific...

Results for the gravitational Wilson loop, in particular the area law for
large loops in the strong coupling region, and the argument for an effective
positive cosmological constant discussed in a previous paper, are extended to
other proposed theories of discrete quantum gravity in the strong coupling
limit. We argue that the area law is a generic...

Plenary talk at the 12-th Marcel Grossman Meeting (MG12) on "Recent Developments in Theoretical and Experimental General Relativity, Astrophysics, and Relativistic Field Theories, UNESCO, Paris (2009)., UNESCO, Paris, France; 07/2009

I review the lattice approach to quantum gravity, and how it relates to the non-trivial ultraviolet fixed point scenario of
the continuum theory. After a brief introduction covering the general problem of ultraviolet divergences in gravity and other
non-renormalizable theories, I discuss the general methods and goals of the lattice approach. An und...

Plenary talk at the 405. WE-Heraeus-Seminar "Quantum Gravity: Challenges and Perspectives" 14 - 16. April 2008, Physikzentrum Bad Honnef, Germany

In a quantum theory of gravity the gravitational Wilson loop, defined as a suitable quantum average of a parallel transport operator around a large near-planar loop, provides important information about the large-scale curvature properties of the geometry. Here we shows that such properties can be systematically computed in the strong coupling limi...

Corrections are computed to the classical static isotropic solution of general relativity, arising from non-perturbative quantum gravity effects. A slow rise of the effective gravitational coupling with distance is shown to involve a genuinely non-perturbative scale, closely connected with the gravitational vacuum condensate, and thereby, it is arg...

I review discrete and continuum approaches to quantized gravity based on the covariant Feynman path integral approach.

Quantum gravity is investigated in the limit of a large number of space-time dimensions, using as an ultraviolet regularization the simplicial lattice path integral formulation. In the weak field limit the appropriate expansion parameter is determined to be $1/d$. For the case of a simplicial lattice dual to a hypercube, the critical point is found...

Quantum corrections to the classical field equations, induced by a scale dependent gravitational constant, are analyzed in the case of the static isotropic metric. The requirement of general covariance for the resulting non-local effective field equations puts severe restrictions on the nature of the solutions that can be obtained. In general the e...

The possibility that the strength of gravitational interactions might slowly increase with distance, is explored by formulating a set of effective field equations, which incorporate the gravitational, vacuum-polarization induced, running of Newton's constant $G$. The resulting long distance (or large time) behaviour depends on only one adjustable p...

Non-perturbative studies of quantum gravity have recently suggested the possibility that the strength of gravitational interactions might slowly increase with distance. Here a set of generally covariant effective field equations are proposed, which are intended to incorporate the gravitational, vacuum-polarization induced, running of Newton's const...

The lattice formulation of quantum gravity provides a natural framework in which nonperturbative properties of the ground state can be studied in detail. In this paper we investigate how the lattice results relate to the continuum semiclassical expansion about smooth manifolds. As an example we give an explicit form for the lattice ground-state wav...

In the continuum the Bianchi identity implies a relationship between different components of the curvature tensor, thus ensuring the internal consistency of the gravitational field equations. In this paper an exact form for the Bianchi identity in Regge's discrete formulation of gravity is derived, by considering appropriate products of rotation ma...

I discuss a model for quantized gravitation based on the simplicial lattice discretization. It has been studied in some detail using a comprehensive finite size scaling analysis combined with renormalization group methods. The results are consistent with a value for the universal critical exponent for gravitation $\nu=1/3$, and suggest a simple rel...

A model for quantized gravitation based on simplicial lattice discretization is studied in detail using a comprehensive finite size scaling analysis combined with renormalization group methods. The results are consistent with a value for the universal critical exponent for gravitation, ν=1/3, and suggest a simple relationship between Newton’s const...

I discuss a model for quantized gravitation based on the simplicial
lattice discretization. It has been studied in detail using a
comprehensive finite size scaling analysis combined with renormalization
group methods. The results are consistent with a value for the universal
critical exponent for gravitation ν = 1/3, and suggest a simple
relationsh...

Functional measures for lattice quantum gravity should agree with their continuum counterparts in the weak field, low momentum limit. After showing that the standard simplicial measure satisfies the above requirement, we prove that a class of recently proposed non-local measures for lattice gravity do not satisfy such a criterion, already to lowest...

Accurate Quantum Gravity calculations, based on the simplicial lattice formulation, are computationally very demanding and require vast amounts of computer resources. A custom-made 64-node parallel super- computer capable of performing up to 2 × 1010 floating point operations per second has been assembled entirely out of commodity components, and h...

The issue of local gauge invariance in the simplicial lattice formulation of gravity is examined. We exhibit explicitly, both in the weak-field expansion about flat space, and subsequently for arbitrarily triangulated background manifolds, the exact local gauge invariance of the gravitational action, which includes in general both cosmological cons...

We develop the general formalism for performing perturbative diagrammatic expansions in the lattice theory of quantum gravity. The results help establish a precise correspondence between continuum and lattice quantities, and should be a useful guide for nonperturbative studies of gravity. The Feynman rules for Regge;s simplicial lattice formulation...

The leading long-distance quantum correction to the Newtonian potential for heavy spinless particles is computed in quantum gravity. The potential is obtained directly from the sum of all graviton exchange diagrams contributing to lowest non-trivial order to the scattering amplitude. The calculation correctly reproduces the leading classical relati...

A model for quantum gravity in one (time) dimension is discussed, based on Regge's discrete formulation of gravity. The nature of exact continuous lattice diffeomorphisms and the implications for a regularized gravitational measure are examined. After introducing a massless scalar field coupled to the edge lengths, the scalar functional integral is...

Some first results are presented regarding the behavior of invariant correlations in simplicial gravity, with an action containing both a bare cosmological term and a lattice higher derivative term. The determination of invariant correlations as a function of geodesic distance by numerical methods is a difficult task, since the geodesic distance be...

We show how the Newtonian potential between two heavy masses can be computed in simplicial quantum gravity. On the lattice we compute correlations between Wilson lines associated with the heavy particles and which are closed by the lattice periodicity. We check that the continuum analog of this quantity reproduces the Newtonian potential in the wea...

A model for quantized gravity coupled to matter in the form of a single scalar field is investigated in four dimensions. For the metric degrees of freedom we employ Regge's simplicial discretization, with the scalar fields defined at the vertices of the four-simplices. We examine how the continuous phase transition found earlier, separating the smo...

I discuss some results we have obtained recently in a lattice model for quantized gravity coupled to scalar matter in four dimensions. We have looked at how the continuous phase transition separating the smooth from the rough phase of gravity is influenced by the presence of the scalar field. We find that close to the critical point, where the aver...

A numerical evaluation of the discrete path integral for pure lattice gravity, with and without higher derivative terms, and using the lattice analog of the DeWitt gravitational measure, shows the existence of a well-behaved ground state for sufficiently strong gravity (G ⩾ Gc). Close to the continuous critical point separating the smooth from the...

I summarize recent results obtained in a four-dimensional model of simplicial quantum gravity based on Regge's discretization, with a higher derivative regulator term. A non-trivial critical point is found at some finite value of the bar Newton's constant, separating the smooth (G > Gc, small negative curvature) from the rough (G < Gc, large positi...

I summarize recent results obtained in a four-dimensional model of simplicial quantum gravity based on Regge's discretization, with a higher derivative regulator term. A non-trivial critical point is found at some finite value of the bare Newton's constant, separating the smooth (G > G(c), small negative curvature) from the rough (G < G(c), large p...

The weak-field expansion and the nonperturbative ground state of three-dimensional simplicial quantum gravity are discussed. The correspondence between lattice and continuum operators is shown in the context of the lattice weak-field expansion, around a simplicial network built of rigid hypercubes, and the lattice translational zero modes are exhib...

According to Einstein's general theory of relativity, the geometric properties of space are related to the distribution of matter and energy in the universe. In a quantum-mechanical theory of gravitation the geometry of space and time is subject to strong fluctuations at extremely short distances. Traditional methods, based on perturbation theory,...

The phase diagram and critical exponents for pure simplicial quantum gravity (Regge calculus) in four dimensions are discussed. In the small-G phase, where G is the bare Newton's constant, the simplices are collapsed and no continuum limit exists. In the large-G phase the ground state appears to be well behaved, and the curvature goes to zero conti...

A model describing Ising spins with short range interactions moving randomly in a plane is considered. In the presence of a hard core repulsion, which prevents the Ising spins from overlapping, the model is analogous to a dynamically triangulated Ising model with spins constrained to move on a flat surface. As a function of coupling strength and ha...

Recent results for simplicial quantum gravity in four dimensions are reviewed. Effects of both higher derivative terms and gravitational measure contributions are investigated. Prospects for solving numerically quantized gravity in four dimensions are discussed.

Recent results for simplicial quantum gravity are reviewed. Models are considered in which the topology is fixed, and the edge lengths are varied while the coordination number is held fixed (‘Regge calculus’). As expected on the basis of universality, in two dimensions the results for pure gravity critical exponents are found to be in agreement wit...

Simplicial higher-derivative quantum gravity is investigated in two dimensions for a manifold of toroidal topology. The manifold is dynamically triangulated using Regge's formulation of gravity, with continuously varying edge lengths and fixed coordination number. Critical exponents are estimated by computer simulation on lattices with up to 786432...

Over the past fifteen years numerical lattice simulations have developed into a promising tool for understanding the complexities of quantum chromodynamics (QCD) at the confinement scale. Among the successes of lattice gauge theory are these:
• The only convincing demonstration of confinement and chiral symmetry breaking, starting from first princ...

A model describing Ising spins with short range interactions moving randomly in a plane is considered. In the presence of a hard core repulsion, which prevents the Ising spins from overlapping, the model is analogous to a dynamically triangulated Ising model with spins constrained to move on a flat surface. It is found that as a function of couplin...

Recent results for simplicial quantum gravity in the Regge formulation
are discussed. While no phase transition is found for pure gravity in
two dimensions, a phase transition between a 'rough' and a 'smooth'
phase of spacetime is found in both three and four dimensions. The
importance of calculating a variety of geometric coordinate invariance
cor...

Recent work on Regge’s lattice formulation of quantum gravity is reviewed. The problem of the lattice transcription of the action and the measure is discussed, and a comparison is made to the expected results in the continuum. The recovery of general coordinate invariance in the continuum is illustrated in the two-dimensional case, where critical e...

We reexamine the difficulties associated with application of the Langevin method to numerical simulation of models with non-positive definite statistical weights, including the Hubbard model. We show how to avoid the violent crossing of the zeroes of the weights and how to move those nodes away from the real axis. However, it still appears necessar...

I present recent results of a simulation of lattice Quantum Chromo-Dynamics with two and three flavors of dynamical Wilson fermions on a 10x10x10x30 lattice. I discuss the source and nature of the systematic error in the pseudofermion method, and ways to reduce the error to an amount which is comparable or less than the expected statistical error....

New results of a large-scale simulation of lattice quantum chromodynamics with three (u,d,s) dynamical Wilson fermions on a 10×10×10×30 space-time lattice are presented. The computations presented here confirm earlier results that indicated the presence of substantial effects due to fermion vacuum-polarization loops. As a check on the results two v...

I present recent results of simulations of lattice Quantum Chromo-Dynamics with two and three flavors of dynamical Wilson fermions on a 10 x 10 x 10 x 30 lattice. I discuss the source and nature of the systematic error in the pseudofermion method, and ways to reduce the error to an amount which is comparable or less than the expected statistical er...