arXiv subjects

Andrzej Herdegen

Publications and source records attributed to Andrzej Herdegen.

25 records · Page 2Linked to original sources

arXiv2005

Quantum backreaction (Casimir) effect. II. Scalar and electromagnetic fields

Casimir effect in most general terms may be understood as a backreaction of a quantum system causing an adiabatic change of the external conditions under which it is placed. This paper is the second installment of a work scrutinizing this effect with the use of algebraic methods in quantum theory. The general scheme worked out in the first part is applied here to the discussion of particular models. We consider models of the quantum scalar field subject to external interaction with ``softened'' Dirichlet or Neumann boundary conditions on two parallel planes. We show that the case of electromagnetic field with softened perfect conductor conditions on the planes may be reduced to the other two. The ``softening'' is implemented on the level of the dynamics, and is not imposed ad hoc, as is usual in most treatments, on the level of observables. We calculate formulas for the backreaction energy in these models. We find that the common belief that for electromagnetic field the backreaction force tends to the strict Casimir formula in the limit of ``removed cutoff'' is not confirmed by our strict analysis. The formula is model dependent and the Casimir value is merely a term in the asymptotic expansion of the formula in inverse powers of the distance of the planes. Typical behaviour of the energy for large separation of the plates in the class of models considered is a quadratic fall-of. Depending on the details of the ``softening'' of the boundary conditions the backreaction force may become repulsive for large separations.

hep-th↗

arXiv2004

Quantum backreaction (Casimir) effect I. What are admissible idealizations?

Casimir effect, in a broad interpretation which we adopt here, consists in a backreaction of a quantum system to adiabatically changing external conditions. Although the system is usually taken to be a quantum field, we show that this restriction rather blurs than helps to clarify the statement of the problem. We discuss the problem from the point of view of algebraic structure of quantum theory, which is most appropriate in this context. The system in question may be any quantum system, among others both finite as infinite dimensional canonical systems are allowed. A simple finite-dimensional model is discussed. We identify precisely the source of difficulties and infinities in most of traditional treatments of the problem for infinite dimensional systems (such as quantum fields), which is incompatibility of algebras of observables or their representations. We formulate conditions on model idealizations which are acceptable for the discussion of the adiabatic backreaction problem. In the case of quantum field models in that class we find that the normal ordered energy density is a well defined distribution, yielding global energy in the limit of a unit test function. Although we see the "zero point" expressions as inappropriate, we show how they can arise in the quantum field theory context as a result of uncontrollable manipulations.

hep-th↗

arXiv2004

Asymptotic algebra of quantum electrodynamics

The Staruszkiewicz quantum model of the long-range structure in electrodynamics is reviewed in the form of a Weyl algebra. This is followed by a personal view on the asymptotic structure of quantum electrodynamics.

hep-th↗

arXiv2003

Is Einstein's equivalence principle valid for a quantum particle?

Einstein's equivalence principle in classical physics is a rule stating that the effect of gravitation is locally equivalent to the acceleration of an observer. The principle determines the motion of test particles uniquely (modulo very broad general assumptions). We show that the same principle applied to a quantum particle described by a wave function on a Newtonian gravitational background determines its motion with a similar degree of uniqueness.

gr-qc↗

arXiv2001

No-nonsense Casimir force

Two thin conducting, electrically neutral, parallel plates forming an isolated system in vacuum exert attracting force on each other, whose origin is the quantum electrodynamical interaction. This theoretical hypothesis, known as Casimir effect, has been also confirmed experimentally. Despite long history of the subject, no completely convincing theoretical analysis of this effect appears in the literature. Here we discuss the effect (for the scalar field) anew, on a revised physical and mathematical basis. Standard, but advanced methods of relativistic quantum theory are used. No anomalous features of the conventional approaches appear. The Casimir quantitative prediction for the force is shown to constitute the leading asymptotic term, for large separation of the plates, of the full, model-dependent expression.

hep-th↗

arXiv1998

Semidirect product of CCR and CAR algebras and asymptotic states in quantum electrodynamics

A C*-algebra containing the CCR and CAR algebras as its subalgebras and naturally described as the semidirect product of these algebras is discussed. A particular example of this structure is considered as a model for the algebra of asymptotic fields in quantum electrodynamics, in which Gauss' law is respected. The appearence in this algebra of a phase variable related to electromagnetic potential leads to the universal charge quantization. Translationally covariant representations of this algebra with energy-momentum spectrum in the future lightcone are investigated. It is shown that vacuum representations are necessarily nonregular with respect to total electromagnetic field. However, a class of translationally covariant, irreducible representations is constructed excplicitly, which remain as close as possible to the vacuum, but are regular at the same time. The spectrum of energy-momentum fills the whole future lightcone, but there are no vectors with energy-momentum lying on a mass hyperboloid or in the origin.

hep-th↗

arXiv1996

Asymptotic algebra for charged particles and radiation

A C*-algebra of asymptotic fields which properly describes the infrared structure in quantum electrodynamics is proposed. The algebra is generated by the null asymptotic of electromagnetic field and the time asymptotic of charged matter fields which incorporate the corresponding Coulomb fields. As a consequence Gauss' law is satisfied in the algebraic setting. Within this algebra the observables can be identified by the principle of gauge invariance. A class of representations of the asymptotic algebra is constructed which resembles the Kulish-Faddeev treatment of electrically charged asymptotic fields.

hep-th↗