Publications (113)378.54 Total impact
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ABSTRACT: We investigate path integral quantization of two versions of unimodular gravity. First a fully diffeomorphisminvariant theory is proposed, which does not include a unimodular condition on the metric, while still being equivalent to other unimodular gravity theories at classical level. The path integral has the same form as in general relativity (GR), except that the cosmological constant is an unspecified value of a variable, and thus unrelated to any coupling constant. When the state of the universe is a superposition of vacuum states, the path integral is extended to include an integral over the cosmological constant. Second, we analyze the standard unimodular theory of gravity, where the metric determinant is fixed by a constraint. Its path integral differs from the one of GR in two ways: the metric of spacetime satisfies the unimodular condition only in average over space, and both the Hamiltonian constraint and the associated gauge condition have zero average over space. Finally, the canonical relation between the given unimodular theories of gravity is established.  [Show abstract] [Hide abstract]
ABSTRACT: It is shown that the neutronantineutron oscillation per se does not necessarily imply CP violation in an effective local Lorentz invariant description of the neutron which preserves CPT, contrary to a recent analysis in the literature. A CP and baryon numberviolating term can be transformed into a CP conserving one, thus rendering the CP violation spurious and unusable in the analysis of baryogenesis, for example. It is also shown that the neutronantineutron oscillation in a $\Delta B=2$, Lorentz and CPT invariant interaction can occur only when parity is violated, irrespective of the CP properties; when parity is conserved, it is the ordinary quantum transition from neutron to antineutron which takes place. Those statements are proven by explicitly analyzing all the possible combinations with P, C and CP violation or their conservation. Moreover, a suitable combination of P=odd and P=even $\Delta B=2$ interactions in the present model is shown to give rise to the CP preserving mass term for the righthanded neutrino if one replaces the neutron by the neutrino, reinforcing the conclusion.  [Show abstract] [Hide abstract]
ABSTRACT: We study modifications of the Schwarzschild solution within the noncommutative gauge theory of gravity. In the present analysis, the deformed solutions are obtained by solving the field equations perturbatively, up to the second order in the noncommutativity parameter $\Theta$, for both exterior and interior solutions of the equations of motion for $e_\mu ^a \left(x\right)$. Remarkably, we find that this new noncommutive solution is analogous to the ReissnerNordstr\"om solution in the ordinary spacetime, in which the square of electric charge is replaced by the square of the noncommutativity parameter, but with opposite sign. This amounts to the noncommutative Schwarzschild radius $r_{NCS}$ becoming larger than the usual radius $r_S =2M$, instead of smaller as it happens to the ReissnerNordstr\"om radius $r_{RN}$, implying that $r_{NCS}>r_{S} >r_{RN}$. An intuitive interpretation of this result is mentioned. 
Article: Neutrinoantineutrino Mass Splitting in the Standard Model: Neutrino Oscillation and Baryogenesis
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ABSTRACT: By adding a neutrino mass term to the Standard Model, which is Lorentz and $SU(2)\times U(1)$ invariant but nonlocal to evade $CPT$ theorem, it is shown that nonlocality within a distance scale of the Planck length, that may not be fatal to unitarity in generic effective theory, can generate the neutrinoantineutrino mass splitting of the order of observed neutrino mass differences, which is tested in oscillation experiments, and nonnegligible baryon asymmetry depending on the estimate of sphaleron dynamics. The oneloop order induced electronpositron mass splitting in the Standard Model is shown to be finite and estimated at $\sim 10^{20}$ eV, well below the experimental bound $< 10^{2}$ eV. The induced $CPT$ violation in the $K$meson in the Standard Model is expected to be even smaller and well below the experimental bound $m_{K}m_{\bar{K}}<0.44\times 10^{18}$ GeV.  [Show abstract] [Hide abstract]
ABSTRACT: We revisit the problem of stability of string vacua involving hyperbolic orbifolds using methods from homotopy theory and Khomology. We propose a definition of Type II string theory on such backgrounds that further carry stratified systems of fiber bundles, which generalise the more conventional orbifold and symmetric string backgrounds, together with a classification of wrapped branes by a suitable generalized homology theory. For spaces stratified fibered over hyperbolic orbifolds we use the algebraic Ktheory of their fundamental groups and Quinn homology to derive criteria for brane stability in terms of an AtiyahHirzebruch type spectral sequence with its lift to Khomology. Stable Dbranes in this setting carry stratified charges which induce new additive structures on the corresponding Khomology groups. We extend these considerations to backgrounds which support Hflux, where we use Kgroups of twisted group algebras of the fundamental groups to analyse stability of locally symmetric spaces with Kamenable isometry groups, and derive stability conditions for branes wrapping the fibers of an EilenbergMacLane spectrum functor.  [Show abstract] [Hide abstract]
ABSTRACT: We develop a selfconsistent $Spin(4,4)$invariant model of the unification of gravity with weak $SU(2)$ gauge and Higgs fields in the visible and invisible sectors of our Universe. We consider a general case of the graviweak unification, including the higherderivative superrenormalizable theory of gravity, which is a unitary, asymptoticallyfree and perturbatively consistent theory of the quantum gravity.  [Show abstract] [Hide abstract]
ABSTRACT: On the basis of a previously proposed mechanism of neutrinoantineutrino mass splitting in the Standard Model, which is Lorentz and $SU(2)\times U(1)$ invariant but nonlocal to evade $CPT$ theorem, we discuss the possible implications of neutrinoantineutrino mass splitting on neutrino physics and baryogenesis. It is shown that nonlocality within a distance scale of the Planck length, that may not be fatal to unitarity in generic effective theory, can generate the neutrinoantineutrino mass splitting of the order of observed neutrino mass differences, which is tested in oscillation experiments, and nonnegligible baryon asymmetry depending on the estimate of sphaleron dynamics. The oneloop order induced electronpositron mass splitting in the Standard Model is shown to be finite and estimated at $\sim 10^{20}$ eV, well below the experimental bound $< 10^{2}$ eV. The induced $CPT$ violation in the $K$meson in the Standard Model is expected to be even smaller and well below the experimental bound $m_{K}m_{\bar{K}}<0.44\times 10^{18}$ GeV.  [Show abstract] [Hide abstract]
ABSTRACT: Recently modified gravitational theories which mimic the behaviour of dark matter, the socalled "Mimetic Dark Matter", have been proposed. We study the consistency of such theories with respect to the absence of ghost instability and propose a new tensorvectorscalar theory of gravity, which is a generalization of the previous models of mimetic dark matter with additional desirable features. In the light of these observations, the idea of mimetic matter is a promising approach to the problem of dark matter.  [Show abstract] [Hide abstract]
ABSTRACT: Among modified gravitational theories, the TensorVectorScalar (TeVeS) occupies a special place  it is a covariant theory of gravity that produces the modified Newtonian dynamics (MOND) in the nonrelativistic weak field limit and explains the astrophysical data by all means better than the GR, at scales larger than that of the Solar System. We show that, in contrast with other modified theories, TeVeS is free from ghosts. These achievements make TeVeS (and its nonrelativistic limit) a viable theory of gravity. A speculative outlook on the emergence of TeVeS from a quantum theory is presented. 
Chapter: Physics and Life
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ABSTRACT: Life sciences are among the most interesting fields of contemporary scientific research. The biological world has such a wide range of complexities that any attempt to present it in any depth would take us outside the scope of the present book. In the present chapter, we shall thus only refer to a few specific physical problems in the biological world. 
Chapter: Electromagnetic Waves
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ABSTRACT: In the previous chapter we saw that an electric charge at rest creates a surrounding static field. A charge moving with constant velocity creates a constant electromagnetic field displacing with the charge. However, an accelerated charge produces a field of a different nature: a radiation field, which propagates far from its source and becomes independent of it. A charge moving at constant velocity is displaced with its field, but does not emit radiation. Charge acceleration is a necessary and sufficient condition for the generation of electromagnetic radiation. We shall see later that radiation behaves in dual form, as waves and as particles (photons), but this chapter will deal mainly with the wave behaviour of radiation.  [Show abstract] [Hide abstract]
ABSTRACT: We construct a model unifying gravity with weak $SU(2)$ gauge and "Higgs" scalar fields. We assume the existence of a visible and an invisible (hidden) sector of the Universe. We used the extension of Plebanski's 4dimensional gravitational theory, in which the fundamental fields are twoforms containing tetrads, spin connections and additional auxiliary fields. Considering a $Spin(4,4)$ invariant extended Plebanski action, we recover the actions in both (visible and invisible) sectors of the Universe. After symmetry breaking of the graviweak (GW) unification, its physical constants (Newton's constants, cosmological constants, YMcouplings, etc.), are determined by a parameter $g_{uni}$ of the GW unification. It is discussed that if this "Higgs" field coming in the GW unification could be the Higgs of the Standard Model, then the idea that its vacuum value could be, according to the Multiple Point Principle, a second minimum of the Higgs field effective potential, turns out not to be viable. Then other scalar "Higgs" field, giving the inflation and axion fields, has a Planck scale expectation value, and could have a better chance of being the scalar field unified with gravity.  [Show abstract] [Hide abstract]
ABSTRACT: We analyze gravitational theories with quadratic curvature terms, including the case of conformally invariant Weyl gravity, motivated by the intention to find a renormalizable theory of gravity in the ultraviolet region, yet yielding general relativity at long distances. In the Hamiltonian formulation of Weyl gravity, the number of local constraints is equal to the number of unstable directions in phase space, which in principle could be sufficient for eliminating the unstable degrees of freedom in the full nonlinear theory. All the other theories of quadratic type are unstable  a problem appearing as ghost modes in the linearized theory. We find that the full projection of the Weyl tensor onto a threedimensional hypersurface contains an additional fully traceless component, given by a quadratic extrinsic curvature tensor. A certain inconsistency in the literature is found and resolved: when the conformal invariance of Weyl gravity is broken by a cosmological constant term, the theory becomes pathological, since a constraint required by the Hamiltonian analysis imposes the determinant of the metric of spacetime to be zero. In order to resolve this problem by restoring the conformal invariance, we introduce a new scalar field that couples to the curvature of spacetime, reminiscent of the introduction of vector fields for ensuring the gauge invariance.  [Show abstract] [Hide abstract]
ABSTRACT: The CPT theorem in quantum field theory, its validity, breaking and consequences are reviewed. One can show that for CPT theorem to hold, Lorentz invariance is not always needed. Also one can have CPT violation, while there is Lorentz invariance. Field theoretical examples for both cases are given and mass differences between particleantiparticle are discussed as well. Unambiguous tests of CPT violation, unrelated to the breaking of Lorentz invariance, are suggested.  [Show abstract] [Hide abstract]
ABSTRACT: We study Mtheory and Dbrane quantum partition functions for microscopic black hole ensembles within the context of the AdS/CFT correspondence in terms of highest weight representations of infinitedimensional Lie algebras, elliptic genera, and Hilbert schemes, and describe their relations to elliptic modular forms. The common feature in our examples lie in the modular properties of the characters of certain representations of the pertinent affine Lie algebras, and in the role of spectral functions of hyperbolic threegeometry associated with qseries in the calculation of elliptic genera. We present new calculations of supergravity elliptic genera on local CalabiYau threefolds in terms of BPS invariants and spectral functions, and also of equivariant Dbrane elliptic genera on generic toric singularities. We use these examples to conjecture a link between the black hole partition functions and elliptic cohomology.  [Show abstract] [Hide abstract]
ABSTRACT: We consider a Graviweak Unification model with the assumption of the existence of the hidden (invisible) sector of our Universe parallel to the visible world. This Hidden World (HW) is assumed to be a Mirror World (MW) with broken mirror parity. We start with a diffeomorphism invariant theory of a gauge field valued in a Lie algebra g, which is broken spontaneously to the direct sum of the spacetime Lorentz algebra and the YangMills algebra: $\tilde {\mathfrak g} = {\mathfrak su}(2)^{(grav)}_L \oplus {\mathfrak su}(2)_L$  in the ordinary world, and $\tilde {\mathfrak g}' = {{\mathfrak su}(2)'}^{(grav)}_R \oplus {\mathfrak su}(2)'_R$  in the hidden world. Using an extension of the Plebanski action for general relativity, we recover the actions for gravity, SU(2) YangMills and Higgs fields in both (visible and invisible) sectors of the Universe, and also the total action. After symmetry breaking, all physical constants, including the Newton's constants, cosmological constants, YangMills couplings, and other parameters, are determined by a single parameter $g$ presented in the initial action, and by the Higgs VEVs. The Dark Energy problem of this model predicts a too large supersymmetric breaking scale ($\sim 10^{10}10^{12}$ GeV), which is not within the reach of the LHC experiments.  [Show abstract] [Hide abstract]
ABSTRACT: We study a Lie algebra of formal vector fields $W_n$ with its application to the perturbative deformed holomorphic symplectic structure in the Amodel, and a CalabiYau manifold with boundaries in the Bmodel. A relevant concept in the vertex operator algebra and the BRST cohomology is that of the elliptic genera (the oneloop string partition function). We show that the elliptic genera can be written in terms of spectral functions of the hyperbolic threegeometry (which inherits the cohomology structure of BRSTlike operator). We show that equivalence classes of deformations are described by a Hochschild cohomology theory of the DGalgebra ${\mathfrak A} = (A, Q)$, $Q =\bar{\partial}+\partial_{\rm deform}$, which is defined to be the cohomology of $(1)^n Q +d_{\rm Hoch}$. Here $\bar{\partial}$ is the initial nondeformed BRST operator while $\partial_{\rm deform}$ is the deformed part whose algebra is a Lie algebra of linear vector fields ${\rm gl}_n$. We discuss the identification of the harmonic structure $(HT^\bullet(X); H\Omega_\bullet(X))$ of affine space $X$ and the group ${\rm Ext}_{X}^n({\cal O}_{\triangle}, {\cal O}_{\triangle})$ (the HKR isomorphism), and bulkboundary deformation pairing. 
Article: Quantum Corrections to BekensteinHawking Black Hole Entropy and Gravity Partition Functions
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ABSTRACT: Algebraic aspects of the computation of partition functions for quantum gravity and black holes in $AdS_3$ are discussed. We compute the subleading quantum corrections to the BekensteinHawking entropy. It is shown that the quantum corrections to the classical result can be included systematically by making use of the comparison with conformal field theory partition functions, via the $AdS_3/CFT_2$ correspondence. This leads to a better understanding of the role of modular and spectral functions, from the point of view of the representation theory of infinitedimensional Lie algebras. Besides, the sum of known quantum contributions to the partition function can be presented in a closed form, involving the PattersonSelberg spectral function. These contributions can be reproduced in a holomorphically factorized theory whose partition functions are associated with the formal characters of the Virasoro modules. We propose a spectral function formulation for quantum corrections to the elliptic genus from supergravity states. 
Article: Mechanics. An intensive course
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ABSTRACT: Mechanics is one of the oldest and at the same time newest disciplines, in the sense that there are methods and principles developed first in mechanics but now widely used in almost all branches of physics: electrodynamics, quantum mechanics, classical and quantum field theory, special and general theory of relativity, etc. More than that, there are some formalisms like Lagrangian and Hamiltonian approaches, which represent the key stone for the development of the abovementioned disciplines. During the last 2025 years, classical mechanics has undergone an important revival associated with the progress in nonlinear dynamics, applications of Noether's theorem and the extension of variational principles in various interdisciplinary sciences (for instance, magnetofluid dynamics). Thus, there ought to exist a book concerned with the applied analytical formalism, first developed in the frame of theoretical mechanics, which has proved to be one of the most efficient tools of investigation in the entire arena of science. The present book is an outcome of the authors' teaching experience over many years in different countries and for different students studying diverse fields of physics. The book is intended for students at the level of undergraduate and graduate studies in physics, engineering, astronomy, applied mathematics and for researchers working in related subjects. We hope that the original presentation and the distribution of the topics, the various applications in many branches of physics and the set of more than 100 proposed problems, shall make this book a comprehensive and useful tool for students and researchers. The present book is an outcome of the authors' teaching experience over many years in different countries and for different students studying diverse fields of physics. The book is intended for students at the level of undergraduate and graduate studies in physics, engineering, astronomy, applied mathematics and for researchers working in related subjects. We hope that the original presentation and the distribution of the topics, the various applications in many branches of physics and the set of more than 100 proposed problems, shall make this book a comprehensive and useful tool for students and researchers. Âİ SpringerVerlag Berlin Heidelberg 2012. All rights are reserved.  [Show abstract] [Hide abstract]
ABSTRACT: An attempt is made to incorporate the electromagnetic interaction in a Lorentz invariant but CPT violating nonlocal model with particleantiparticle masssplitting, which is regarded as a modified QED. The gauge invariance is maintained by the Schwinger nonintegrable phase factor but the electromagnetic interaction breaks C, CP and CPT symmetries. Implications of the present CPT breaking scheme on the electromagnetic transitions and particleantiparticle pair creation are discussed. The CPT violation such as the one suggested here may open a new path to the analysis of baryon asymmetry since some of the Sakharov constraints are expected to be modified.
Publication Stats
3k  Citations  
378.54  Total Impact Points  
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Institutions

20002015

University of Helsinki
 • Department of Physics
 • Department of Physical Sciences
Helsinki, Uusimaa, Finland
