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John R. Klauder

Publications and source records attributed to John R. Klauder.

118 records · Page 7Linked to original sources
arXiv1996

Coordinate-free quantization of first-class constrained systems

The coordinate-free formulation of canonical quantization, achieved by a flat-space Brownian motion regularization of phase-space path integrals, is extended to a special class of closed first-class constrained systems that is broad enough to include Yang-Mills type theories with an arbitrary compact gauge group. Central to this extension are the use of coherent state path integrals and of Lagrange multiplier integrations that engender projection operators onto the subspace of gauge invariant states.

hep-th↗
arXiv1996

Coherent State Path Integrals for Systems with Constraints

We outline the principal results of a recent examination of the quantization of systems with first- and second-class constraints from the point of view of coherent-state phase-space path integration. Two examples serve to illustrate the procedures.

quant-ph↗
arXiv1996

New Measures for the Quantization of Systems with Constraints

Based on the results of a recent reexamination of the quantization of systems with first-class and second-class constraints from the point of view of coherent-state phase-space path integration, we give additional examples of the quantization procedure for reparameterization invariant Hamiltonians, for systems for which the original set of Lagrange multipliers are elevated to dynamical variables, as well as extend the formalism to include cases of first-class constraints the operator form of which have a spectral gap about the value zero that characterizes the quantum constraint subspace.

quant-ph↗
arXiv1996

Is Quantization Geometry?

The metric known to be relevant for standard quantization procedures receives a natural interpretation and its explicit use simultaneously gives both physical and mathematical meaning to a (coherent-state) phase-space path integral, and at the same time establishes a fully satisfactory, geometric procedure of quantization.

quant-ph↗
arXiv1996

Coherent State Quantization of Constraint Systems

A careful reexamination of the quantization of systems with first- and second-class constraints from the point of view of coherent-state phase-space path integration reveals several significant distinctions from more conventional treatments. Most significantly, we emphasize the importance of using path-integral measures for Lagrange multipliers which ensure that the quantum system satisfies the quantum constraint conditions. Our procedures involve no delta-functionals of the classical constraints, no need for gauge fixing of first-class constraints, no need to eliminate second-class constraints, no potentially ambiguous determinants, and have the virtue of resolving differences between canonical and path-integral approaches. Several examples are considered in detail.

quant-ph↗
arXiv1995

Poisson Distributions for Sharp-Time Fields: Antidote for Triviality

Standard lattice-space formulations of quartic self-coupled Euclidean scalar quantum fields become trivial in the continuum limit for sufficiently high space-time dimensions, and in particular the moment generating functional for space-time smeared fields becomes a Gaussian appropriate to that of a (possibly generalized) free field. For sharp-time fields this fact implies that the ground-state expectation functional also becomes Gaussian in the continuum limit. To overcome these consequences of the central limit theorem, an auxiliary, nonclassical potential is appended to the original lattice form of the model and parameters are tuned so that a generalized Poisson field distribution emerges in the continuum limit for the ground-state probability distribution. As a consequence, the sharp-time expectation functional is infinitely divisible, but the Hamiltonian operator is such, in the general case, that the generating functional for the space-time smeared field is not infinitely divisible in Minkowski space. This feature permits the models in question to escape a manifestly trivial scattering matrix imposed on all infinitely divisible covariant Minkowski fields. Two sequentially related proposals for an alternative lattice formulation of interacting covariant models in four and more space-time dimensions are analyzed in some detail.

hep-th↗
arXiv1995

Coherent States for the Hydrogen Atom

The long-standing problem of finding coherent states for the (bound state portion of the) hydrogen atom is positively resolved. The states in question: (i) are normalized and are parameterized continuously, (ii) admit a resolution of unity with a positive measure, and (iii) enjoy the property that the temporal evolution of any coherent state by the hydrogen atom Hamiltonian remains a coherent state for all time.

quant-ph↗
arXiv1995

Isolation and Expulsion of Divergences in Quantum Field Theory

Divergences that arise in the quantization of scalar quantum field models by means of a lattice-space functional integration may be attributed to a single integration variable, and this fact is demonstrated by showing that if the integrand for that single integration variable is appropriately changed, then a perturbation expansion becomes order-by-order finite and divergence free. The paper concludes with a brief review of a current proposal of how an auxiliary, nonclassical potential added to the lattice action of a relativistic scalar field quantization may automatically render an analogous change of the integrand, and thus may lead, as well, to nontrivial and divergence-free results.

quant-ph↗
arXiv1993

Landau Level Ground--State Degeneracy, and Its Relevance for a General Quantization Procedure

The quantum dynamics of a two-dimensional charged spin $1/2$ particle is studied for general, symmetry--free curved surfaces and general, nonuniform magnetic fields that are, when different from zero, orthogonal to the defining two surface. Although higher Landau levels generally lose their degeneracy under such general conditions, the lowest Landau level, the ground state, remains degenerate. Previous discussions of this problem have had less generality and/or used supersymmetry, or else have appealed to very general mathematical theorems from differential geometry. In contrast our discussion relies on simple and standard quantum mechanical concepts. The mathematical similarity of the physical problem at hand and that of a phase-space path integral quantization scheme of a general classical system is emphasized. Adopting this analogy in the general case leads to a general quantization procedure that is invariant under general coordinate transformations-- completely unlike any of the conventional quantization prescriptions -- and therefore generalizes the concept of quantization to new and hitherto inaccesible situations. In a complementary fashion , the so-obtained picture of general quantization helps to derive useful semiclassical formulas for the Hall current in the case of a filling factor equal to one for a general surface and magnetic field.

gr-qc↗