L. Lanz

• Retired Professor of the University of Milan
• University of Milan

In this paper, we provide a consistent framework to address the notorious difficult decomposition of the single-photon total angular momentum (TAM) into a spin (SAM) and an orbital (OAM) component. We discuss the canonical decomposition into SAM and OAM components, which are the generators of internal and spatial rotations in the space of physical...

We propose a procedure for defining all single-photon observables in terms of Positive-Operator Valued Measures (POVMs), in particular spin and position. We identify the suppression of 0-helicity photon states as a projection from an extended Hilbert space onto the photon Hilbert space. We show that all single-photon observables are in general desc...

The design of advanced machines working in the quantum regime (ELI-NP, IRIDE, e − γ and γ − γ colliders) requires to set the fundamentals needed to have an accurate prediction of the radiation qualities after the Compton scattering. Due to the high energy of the electron beam in the cases above mentioned, the quantum effects, referred as inverse Co...

The design of advanced machines working in the quantum regime (ELI-NP, IRIDE, e - γ and γ - γ colliders) requires to set the fundamentals needed to have an accurate prediction of the radiation qualities after the Compton scattering. Due to the high energy of the electron beam in the cases above mentioned, the quantum effects, referred as inverse Co...

We stress the notion of statistical experiment, which is mandatory for quantum mechanics, and recall Ludwig's foundation of quantum mechanics, which provides the most general framework to deal with statistical experiments giving evidence for particles. In this approach particles appear as interaction carriers between preparation and registration ap...

We come back to the rooting of quantum theory in an objectively given phenomenological context, as it was first sustained by Bohr and later taken by Ludwig as basic motivation of his axiomatic approach. It is shown that the question of compatibility of an objective phenomenological context with present day quantum theory can be answered in a positi...

Thermodynamics of irreversible processes is taken as the phenomenological starting point for the description of macroscopic systems in quantum mechanics and state parameters, which are amenable to be attributed an objective meaning, are introduced inside non relativistic quantum field theory when the macroscopic system is locally at equilibrium. Co...

We argue that the consistency problem between quantum theory and macro- scopic objectivity must be placed inside a quantum description of macroscopic non-equilibrium systems. Resorting to thermodynamic concepts inside quantum eld theory seems to be necessary. 1 The problem of measurement, where does it lead? Discussions on the measurement problem i...

It is argued that the appropriate framework to describe a microsystem as a correlation carrier between a source and a detector is non-equilibrium statistical mechanics for the compound source-detector system. An attempt is given to elucidate how this idealized notion of microsystem might arise inside a field theoretical description of isolated macr...

In this paper we address the problem to give a concrete support to the idea, originally stemming from Niels Bohr, that quantum mechanics must be rooted inside the physics of macroscopic systems. It is shown that, starting from the formalism of the nonequilibrium statistical operator, which is now a consolidated part of quantum statistical mechanics...

An approach to the description of subdynamics inside the nonrelativistic quantum field theory is presented, in which the notions of relevant observable, time scale and complete positivity of the time evolution are stressed. A scattering theory derivation of the subdynamics of a microsystem interacting through collisions with a macrosystem is given,...

For an isolated macrosystem classical state parameters ζ(t) are introduced inside a quantum mechanical treatment. By a suitable mathematical representation of the actual preparation procedure in the time interval [T, t0] a statistical operator is constructed as a solution of the Liouville—von Neumann equation, exhibiting at time t the state paramet...

The relationship between microsystems and macrosystems is considered in the context of quantum field formulation of statistical mechanics: it is argued that problems on foundations of quantum mechanics can be solved relying on this relationship. This discussion requires some improvement of non-equilibrium statistical mechanics that is briefly prese...

Inside quantum mechanics the problem of decoherence for an isolated, finite system is linked to a coarse-grained description of its dynamics.

For an isolated macrosystem classical state parameters $\zeta(t)$ are introduced inside a quantum mechanical treatment. By a suitable mathematical representation of the actual preparation procedure in the time interval $[T,t_0]$ a statistical operator is constructed as a solution of the Liouville von Neumann equation, exhibiting at time $t$ the sta...

Coherent and incoherent neutron-matter interaction is studied inside a recently introduced approach to subdynamics of a macrosystem. The equation describing the interaction is of the Lindblad type and using the Fermi pseudopotential we show that the commutator term is an optical potential leading to well-known relations in neutron optics. The other...

It is argued that setting isolated systems as primary scope of field theory and looking at particles as derived entities, the problem of an objective anchorage of quantum mechanics can be solved and irreversibility acquires a fundamental role. These general ideas are checked in the case of the Boltzmann description of a dilute gas. Comment: 13 page...

It is argued that the dynamics of an isolated system, due to the concrete procedure by which it is separated from the environment, has a non-Hamiltonian contribution. By a unified quantum field theoretical treatment of typical subdynamics, e.g., hydrodynamics, kinetic theory, master equation for a particle interacting with matter, we look for the s...

The meaning of statistical experiments with single microsystems in quantum mechanics is discussed and a general model in the framework of non-relativistic quantum field theory is proposed, to describe both coherent and incoherent interaction of a single microsystem with matter. Compactly developing the calculations with superoperators, it is shown...

In the more refined description of concrete measuring procedures that is allowed by modern quantum theory, objectivity elements can be recovered that are usually deemed to be forbidden in quantum mechanics; actually, in the case of amacrosystem, a way towards an objective physical description appears.

For a macrosystem a general formalism is given, inside quantum field theory, to describe its separation from the surrounding and its time evolution. Assuming a suitable dissipative behaviour of the time evolution of the separated system, an objective quantum description is extracted from quantum field theory, based on a natural set of non-local hid...

A generalised stochastic process is obtained for the Boltzmann distribution function in quantum mechanics: this is an example of an objective state-space description of a quantum system.

A Boltzmann operator is constructed representing an observable for a direct measurement of Boltzmann functions. This operator overcomes all the pathological features inherent in the Wigner function hitherto used in the quantum mechanical derivation of the Boltzmann equation. With the help of this Boltzmann operator a Boltzmann equation, with a new...

In Quantum Mechanics, as well known, due to the occurrence of the so called interference terms, any statement has to refer to a definite experiment performed on an object, i.e. to the response of a specific apparatus. No unambiguous meaning can be attached to statements on the value of any quantity independently of an explicit measurement of it.

First a short review of the generalized formulation of Quantum Mechanics based on the ideas of effect and operation is given and its justification in the framework of a realistic theory of measurement discussed. Then an account is presented of the formalism of the Operation Valued Stochastic Processes which has been recently developed for treating...

A formalism developed in previous papers for the description of continual observations of some quantities in the framework of quantum mechanics is reobtained and generalized, starting from a more axiomatic point of view. The statistics of the observations of continuous state trajectories is treated from the beginning as a generalized stochastic pro...

Starting from the idea of generalized observables, related to effect-valued measures, as introduced by Ludwig, some examples oi continual observations in quantum mechanics are discussed. A functional probability distribution, on the set of the trajectories which are obtained as output of the continual observation, is constructed in the form of a Fe...

A procedure is developed to obtain a joint probability distribution for a set of noncommuting observables. On one side this procedure is a generalization of methods of statistical thermodynamics, on the other one it is linked to Ludwig's generalization of the axiomatics of quantum mechanics. The Gaussian approximation of our probability distributio...

Summary The relationship between the classical description of a macrosystem and quantum mechanics of its particles is considered within the framework recently developed by Ludwig. A procedure is given to define probability measures on the trajectory space of a macrosystem which yields a statistical description of the dynamics of a macrosystem. The...

Physical consequences of a more general theory of symmetries, based on the Galilei semi-group, are investigated for an isolated quantum system. The existence of the fundamental constants of motion is no longer a consequence of the symmetry, but it is an additional requirement. The usual description of a free particle is fully recovered, but a more...

In this paper we justify the use of nonunitary representations of the space−time symmetry group to describe physical systems, as, e.g., unstable particles. It is shown that such a generalization of the standard theory of symmetries is possible inside the approach to quantum mechanics recently developed by Ludwig. The Poincare´ semigroup turns out t...

Some unpleasant features of the usual treatment of irreversible processes in quantum mechanics are discussed. It is shown how the description of a non-relativistic unstable particle can be cleanly embedded into a reversible Galilean quantum field theory. It is proven that in the case of stable particles the embedding procedure gives the same values...

The procedure devised in a previous paper to obtain the exponential decay law for an unstable non-relativistic isolated particle within a Galilean Quantum Field Theory is applied to describe the transition from the particle to its decay products, as well as the transitions occurring in scattering processes.

The usual treatment of decaying non-relativistic particles by means of a non-unitary irreducible representation of the Galilei group is deduced from a suitable formulation of symmetry principles. In such a formulation time translation is distinguished from time evolution; this point is crucial to obtain the irreversible behaviour of unstable partic...

A general theorem is deduced which illuminates the problem of extracting reduced dynamics from the general dynamics of a system. The Liouville-space formalism is used throughout. The results are applied to the problem of deducing a self-contained description for the time evolution of the macroscopic observables of a microscopic system.By our treatm...

A contribution is given to the attempts towards a solution of the measurement problem in quantum mechanics, in the spirit of some previous papers. In order to justify the possibility of a macroscopic description of the measuring apparatus, a relevant hypothesis is found to be the separation of two characteristic times: the decay time for the kernel...

The part Φ0(t) of the statistical operator (or density function) which is relevant for the description of macroscopic dynamics is treated. The new mathematical properties of the solution of Zwanzig's generalized master equation which are important for the deduction of a markoffian master equation for Φ0(t) are pointed out. On the basis of such resu...

Without Abstract

The solution of the generalized master equation for a macroscopic insulated system is studied in the limit t → + ∞. Using the theory of holomorphic operators in finite-dimensional linear spaces, the spectral properties of the kernel of the G.M.E. are analyzed. It is shown that, under proper conditions, the asymptotic expectation values of the macro...

The solution of the generalized master equation of Zwanzig for a macroscopic system, is approximated by the solution of a markoffian master equation. The reliability of this approximation is studied at arbitrary times.

To give a macroscopic description of a system, a suitable assumption is generally made on the initial statistical operator. We look for the situation in which the Liouville-von Neumann equation implies that an initial condition of such type can be again assumed at time t1, once it has been assumed at some time t0< t1. It is pointed out that, on the...

Summary Given a functionf(z) expressed through a dispersion integral with a spectral function ϱ(ξ), a theorem is established which provides an asymptotic bound forf(z), once given asymptotic bounds to ϱ(ξ) and ϱ’(ξ). The result is applied to the discussion of the asymptotic behaviour of the partial wave and the total scattering amplitudes.

The energy conservation in the motion of a radiating electron is studied by means of the finite differences equation proposed by Caldirola. The acceleration energy or the Schott’s energy, that occurs in the classical theory of Dirac-Eliezer, does no longer appear in the conservation equation. The rate of radiated energy reduces to an obvious relati...