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Papers by Alex Calogeracos

Physics of Atomic Nuclei, Oct 9, 1995

A second quantised theory of electrons and positrons in a deep time-dependent potential well is d... more A second quantised theory of electrons and positrons in a deep time-dependent potential well is discussed. It is shown that positron production from the well is a natural consequence of Dirac's hole theory when the strength of the well becomes supercritical. A formalism is developed whereby the amplitude for emission of a positron of a given momentum can be calculated. The difference between positron production and electron-positron pair production is demonstrated. Considerations of the vacuum charge and of Levinson's theorem are required for a full description of the problem.

We investigate a commonly used formula which seems to give non-integral vacuum charge in the cont... more We investigate a commonly used formula which seems to give non-integral vacuum charge in the continuum limit. We show that the limit is subtle and care must be taken to get correct results.

We address the question of radiation emission from both perfect and dispersive mirrors following ... more We address the question of radiation emission from both perfect and dispersive mirrors following prescribed relativistic trajectories. The trajectories considered are asymptotically inertial: the mirror starts from rest and eventually reverts to motion at uniform velocity. This enables us to provide a description in terms of in and out states. We calculate exactly the Bogolubov alpha and beta coefficients for a specific form of the trajectory, and stress the analytic properties of the amplitudes and the constraints imposed by unitarity. A formalism for the description of emission of radiation from a dispersive mirror is presented.

Ijmpa, May 14, 2002

The question is examined of a mirror which starts from rest and either (i) accelerates for some t... more The question is examined of a mirror which starts from rest and either (i) accelerates for some time and eventually reverts to motion at constant velocity, (ii) continues accelerating forever. A sharp distinction in made between cases (i) and (ii) concerning the spectrum of the emitted radiation, and the qualitative difference between the two cases is pointed out. The Bogolubov coefficients are calculated for a trajectory of type (i). A type (ii) trajectory is entirely unphysical as far as any realistic mirror is concerned, however it is of interest in that it has been used as a simple analog of black hole collapse. The spectrum emitted for the type (ii) trajectory z = -ln(cosh t) is examined and it is shown that it is indeed that of a black body. Inconsistencies in previous derivations of the above result are pointed out.

We address the question of radiation emitted from a collapsing star. We consider the simple model... more We address the question of radiation emitted from a collapsing star. We consider the simple model of a spherical star consisting of pressure-free dust and we derive the emission spectrum via a systematic asymptotic expansion of the complete Bogolubov amplitude. We present a review of standard features of the problem and we point out certain inconsistencies in previous derivations.

The interaction of a fast moving sine-Gordon soliton with an external periodic potential is exami... more The interaction of a fast moving sine-Gordon soliton with an external periodic potential is examined. The resulting equation of motion for the collective coordinate representing the position of the soliton is given in relativistic form. We examine the radiation emitted due to the interaction of the soliton with the potential and we calculate the potential dependent part of the time evolution equation for the creation and annihilation operators for fluctuations.

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 1996

ABSTRACT We consider the state vector of a system containing a particle, in the approximation tre... more ABSTRACT We consider the state vector of a system containing a particle, in the approximation treating the particle (mass = m) as if it followed a classically prescribed trajectory R(t). Since a real particle has position and momentum operators r and p of its own, one must find a way effectively to demote these from dynamical variables to mere time-dependent parameters. The traditional method is to subject the Hamiltonian system to a formal constraint r - R(t) = 0. Here we consider instead the particle trapped in a sufficiently tight-binding potential V(r - R(t)); the conclusions remain the same but the reasoning becomes much more accessible. The state vector acquires an overall phase factor exp{-i intt dt'(-1/2mR2(t'))}, surprising in that the integrand features not the enforced kinetic energy, but its negative. We elucidate the physics of this phase factor, sketch a scenario for verifying it experimentally and show that it persists essentially unchanged when the trapped particle is coupled to the Maxwell field. The standard adiabatic approximation routinely applied misses this factor altogether, but a more careful modification recovers the right result.

Physical Review Letters, 2000

Physical Review D, 1995

This paper is devoted to a study of possible scaling laws, and their logarithmic corrections, occ... more This paper is devoted to a study of possible scaling laws, and their logarithmic corrections, occurring in deep inelastic electropion production. Both the exclusive and semiexclusive processes are considerd. Scaling laws, originally motivated from PCAC and current algebra ...

Physical Review D, 1990

ABSTRACT We examine the problem of the center-of-mass motion in nonlinear field theories that sup... more ABSTRACT We examine the problem of the center-of-mass motion in nonlinear field theories that support classical static solutions. As a concrete example we consider the model of Goldstone and Jackiw. The total Hamiltonian is separated into three terms: one describing a free kink (baryon) moving with constant arbitrary (not necessarily small) velocity, a second term describing free fluctuations (mesons), and a third term describing the baryon-meson interaction. Total momentum conservation is ensured and the treatment is relativistically covariant. We present the classical theory and also a method which allows the construction of a quantized Hamiltonian and of asymptotic states consisting of one baryon and many mesons. The formalism can then be used for the calculation of {ital S}-matrix elements. The passage from the classical to the quantum theory requires the introduction of unphysical (ghost) states. The principles of the method can be applied to theories in higher spacetime dimensions.

Physica B: Condensed Matter, 1998

Molecular Physics, 1993

ABSTRACT The problem of collective molecular coordinates is examined within the Hamiltonian forma... more ABSTRACT The problem of collective molecular coordinates is examined within the Hamiltonian formalism by enlarging the number of degrees of freedom and transforming the model to a gauge theory (a theory where the solutions to the equations of motion include arbitrary functions of time). It turns out that in the case of a nonlinear molecule and within the harmonic approximation the most appropriate gauge fixing conditions are the Eckart conditions; thus the Wilson-Howard Hamiltonian is derived. The case of a linear molecule is examined as a second application, and it is found that there are two reasonable gauge choices. The question of the linear molecule as the limiting case of a nonlinear one is also elucidated.

Journal of Physics A: Mathematical and Theoretical, 2008

We use elementary time-dependent perturbation theory, referred wholly to an inertial (laboratory)... more We use elementary time-dependent perturbation theory, referred wholly to an inertial (laboratory) frame, to determine the probability that a semi-realistically modelled atom is promoted from the ground to an excited state, with the emission of a photon, when its nucleus is constrained to follow a classically prescribed trajectory including a finite interval of (arbitrary) acceleration between asymptotically uniform initial and final motions. In the formal limit where the proper acceleration alpha is constant and lasts forever, we verify the Unruh effect, namely that the atom then behaves as if it had been exposed to black-body radiation at temperature TU = planckalpha/2pickB. The point is that in virtue of its simplicity our formalism is reasonably adaptable, and its predictions free of objections like those often and rightly based on the unrealizable nature of strictly constant alpha considered directly rather than as a limit.

Journal of Physics A: Mathematical and General, 2002

ABSTRACT We address the question of radiation emission from both perfect and dispersive mirrors f... more ABSTRACT We address the question of radiation emission from both perfect and dispersive mirrors following prescribed relativistic trajectories. The trajectories considered are asymptotically inertial: the mirror starts from rest and eventually reverts to motion at uniform velocity. This enables us to provide a description in terms of in and out states. We calculate exactly the Bogolubov alpha and beta coefficients for a specific form of the trajectory, and stress the analytic properties of the amplitudes and the constraints imposed by unitarity. A formalism for the description of emission of radiation from a dispersive mirror is presented. Comment: 7 figures

Journal of Optics B: Quantum and Semiclassical Optics, 2005

ABSTRACT We consider the bound state of a scalar nucleus and a spin 1/2 electron interacting cova... more ABSTRACT We consider the bound state of a scalar nucleus and a spin 1/2 electron interacting covariantly with a scalar radiation field. The nucleus follows a prescribed relativistic trajectory. The description is wholly in terms of laboratory quantities. The aim of the paper is twofold. We show from first principles how electronic wavefunctions and atomic transition rates transform in accordance with relativistic requirements in the case of uniform nuclear motion. We also present a general expression for the transition probability when the nucleus performs a prescribed accelerated motion.

Journal of Experimental and Theoretical Physics, 1999