9,628 research outputs found
Multipole interaction between atoms and their photonic environment
Macroscopic field quantization is presented for a nondispersive photonic
dielectric environment, both in the absence and presence of guest atoms.
Starting with a minimal-coupling Lagrangian, a careful look at functional
derivatives shows how to obtain Maxwell's equations before and after choosing a
suitable gauge. A Hamiltonian is derived with a multipolar interaction between
the guest atoms and the electromagnetic field. Canonical variables and fields
are determined and in particular the field canonically conjugate to the vector
potential is identified by functional differentiation as minus the full
displacement field. An important result is that inside the dielectric a dipole
couples to a field that is neither the (transverse) electric nor the
macroscopic displacement field. The dielectric function is different from the
bulk dielectric function at the position of the dipole, so that local-field
effects must be taken into account.Comment: 17 pages, to be published in Physical Review
Quantum field theory as eigenvalue problem
A mathematically well-defined, manifestly covariant theory of classical and
quantum field is given, based on Euclidean Poisson algebras and a
generalization of the Ehrenfest equation, which implies the stationary action
principle. The theory opens a constructive spectral approach to finding
physical states both in relativistic quantum field theories and for flexible
phenomenological few-particle approximations.
In particular, we obtain a Lorentz-covariant phenomenological multiparticle
quantum dynamics for electromagnetic and gravitational interaction which
provides a representation of the Poincare group without negative energy states.
The dynamics reduces in the nonrelativistic limit to the traditional
Hamiltonian multiparticle description with standard Newton and Coulomb forces.
The key that allows us to overcome the traditional problems in canonical
quantization is the fact that we use the algebra of linear operators on a space
of wave functions slightly bigger than traditional Fock spaces.Comment: 32 page
Self-consistent theory of large amplitude collective motion: Applications to approximate quantization of non-separable systems and to nuclear physics
The goal of the present account is to review our efforts to obtain and apply
a ``collective'' Hamiltonian for a few, approximately decoupled, adiabatic
degrees of freedom, starting from a Hamiltonian system with more or many more
degrees of freedom. The approach is based on an analysis of the classical limit
of quantum-mechanical problems. Initially, we study the classical problem
within the framework of Hamiltonian dynamics and derive a fully self-consistent
theory of large amplitude collective motion with small velocities. We derive a
measure for the quality of decoupling of the collective degree of freedom. We
show for several simple examples, where the classical limit is obvious, that
when decoupling is good, a quantization of the collective Hamiltonian leads to
accurate descriptions of the low energy properties of the systems studied. In
nuclear physics problems we construct the classical Hamiltonian by means of
time-dependent mean-field theory, and we transcribe our formalism to this case.
We report studies of a model for monopole vibrations, of Si with a
realistic interaction, several qualitative models of heavier nuclei, and
preliminary results for a more realistic approach to heavy nuclei. Other topics
included are a nuclear Born-Oppenheimer approximation for an {\em ab initio}
quantum theory and a theory of the transfer of energy between collective and
non-collective degrees of freedom when the decoupling is not exact. The
explicit account is based on the work of the authors, but a thorough survey of
other work is included.Comment: 203 pages, many figure
Time Evolution In Macroscopic Systems. II: The Entropy
The concept of entropy in nonequilibrium macroscopic systems is investigated
in the light of an extended equation of motion for the density matrix obtained
in a previous study. It is found that a time-dependent information entropy can
be defined unambiguously, but it is the time derivative or entropy production
that governs ongoing processes in these systems. The differences in physical
interpretation and thermodynamic role of entropy in equilibrium and
nonequilibrium systems is emphasized and the observable aspects of entropy
production are noted. A basis for nonequilibrium thermodynamics is also
outlinedComment: 28 page
Geodetic Brane Gravity
Within the framework of geodetic brane gravity, the Universe is described as
a 4-dimensional extended object evolving geodetically in a higher dimensional
flat background. In this paper, by introducing a new pair of canonical fields
{lambda, P_{lambda}}, we derive the quadratic Hamiltonian for such a brane
Universe; the inclusion of matter then resembles minimal coupling. Second class
constraints enter the game, invoking the Dirac bracket formalism. The algebra
of the first class constraints is calculated, and the BRST generator of the
brane Universe turns out to be rank-1. At the quantum level, the road is open
for canonical and/or functional integral quantization. The main advantages of
geodetic brane gravity are: (i) It introduces an intrinsic, geometrically
originated, 'dark matter' component, (ii) It offers, owing to the Lorentzian
bulk time coordinate, a novel solution to the 'problem of time', and (iii) It
enables calculation of meaningful probabilities within quantum cosmology
without any auxiliary scalar field. Intriguingly, the general relativity limit
is associated with lambda being a vanishing (degenerate) eigenvalue.Comment: 23 pages, 1 figure, minor change
On the emergence of gauge structures and generalized spin when quantizing on a coset space
It has been known for some time that there are many inequivalent
quantizations possible when the configuration space of a system is a coset
space G/H. Viewing this classical system as a constrained system on the group
G, we show that these inequivalent quantizations can be recovered from a
generalization of Dirac's approach to the quantization of such a constrained
system within which the classical first class constraints (generating the
H-action on G) are allowed to become anomalous (second class) when quantizing.
The resulting quantum theories are characterized by the emergence of a
Yang-Mills connection, with quantized couplings, and new 'spin' degrees of
{}freedom. Various applications of this procedure are presented in detail:
including a new account of how spin can be described within a path-integral
formalism, and how on S^4 chiral spin degrees of {}freedom emerge, coupled to a
BPST instanton.Comment: 64 pages, plain TeX, DIAS-STP-93-1
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