124 research outputs found
Quantum phases in entropic dynamics
In the Entropic Dynamics framework the dynamics is driven by maximizing
entropy subject to appropriate constraints. In this work we bring Entropic
Dynamics one step closer to full equivalence with quantum theory by identifying
constraints that lead to wave functions that remain single-valued even for
multi-valued phases by recognizing the intimate relation between quantum
phases, gauge symmetry, and charge quantization.Comment: Presented at MaxEnt 2017, the 37th International Workshop on Bayesian
Inference and Maximum Entropy Methods in Science and Engineering (July 9-14,
2017, Jarinu, Brazil
Vortex lines of the electromagnetic field
Relativistic definition of the phase of the electromagnetic field, involving
two Lorentz invariants, based on the Riemann-Silberstein vector is adopted to
extend our previous study [I. Bialynicki-Birula, Z. Bialynicka-Birula and C.
Sliwa, Phys. Rev. A 61, 032110 (2000)] of the motion of vortex lines embedded
in the solutions of wave equations from Schroedinger wave mechanics to Maxwell
theory. It is shown that time evolution of vortex lines has universal features;
in Maxwell theory it is very similar to that in Schroedinger wave mechanics.
Connection with some early work on geometrodynamics is established. Simple
examples of solutions of Maxwell equations with embedded vortex lines are
given. Vortex lines in Laguerre-Gaussian beams are treated in some detail.Comment: 11 pages, 6 figures, to be published in Phys. Rev.
On Clifford Subalgebras, Spacetime Splittings and Applications
Z2-gradings of Clifford algebras are reviewed and we shall be concerned with
an alpha-grading based on the structure of inner automorphisms, which is
closely related to the spacetime splitting, if we consider the standard
conjugation map automorphism by an arbitrary, but fixed, splitting vector.
After briefly sketching the orthogonal and parallel components of products of
differential forms, where we introduce the parallel [orthogonal] part as the
space [time] component, we provide a detailed exposition of the Dirac operator
splitting and we show how the differential operator parallel and orthogonal
components are related to the Lie derivative along the splitting vector and the
angular momentum splitting bivector. We also introduce multivectorial-induced
alpha-gradings and present the Dirac equation in terms of the spacetime
splitting, where the Dirac spinor field is shown to be a direct sum of two
quaternions. We point out some possible physical applications of the formalism
developed.Comment: 22 pages, accepted for publication in International Journal of
Geometric Methods in Modern Physics 3 (8) (2006
Maximally Causal Quantum Mechanics
We present a new causal quantum mechanics in one and two dimensions developed
recently at TIFR by this author and V. Singh. In this theory both position and
momentum for a system point have Hamiltonian evolution in such a way that the
ensemble of system points leads to position and momentum probability densities
agreeing exactly with ordinary quantum mechanics.Comment: 7 pages,latex,no figures,to appear in Praman
Thermodynamic Gravity and the Schrodinger Equation
We adopt a 'thermodynamical' formulation of Mach's principle that the rest
mass of a particle in the Universe is a measure of its long-range collective
interactions with all other particles inside the horizon. We consider all
particles in the Universe as a 'gravitationally entangled' statistical ensemble
and apply the approach of classical statistical mechanics to it. It is shown
that both the Schrodinger equation and the Planck constant can be derived
within this Machian model of the universe. The appearance of probabilities,
complex wave functions, and quantization conditions is related to the
discreetness and finiteness of the Machian ensemble.Comment: Minor corrections, the version accepted by Int. J. Theor. Phy
Stationary Flows of the Parabolic Potential Barrier in Two Dimensions
In the two-dimensional isotropic parabolic potential barrier , though it is a model of an unstable system in quantum
mechanics, we can obtain the stationary states corresponding to the real energy
eigenvalue . Further, they are infinitely degenerate. For the first few
eigenstates, we will find the stationary flows round a right angle that are
expressed by the complex velocity potentials .Comment: 12 pages, AmS-LaTeX, 4 figure
Applications of Two-Body Dirac Equations to the Meson Spectrum with Three versus Two Covariant Interactions, SU(3) Mixing, and Comparison to a Quasipotential Approach
In a previous paper Crater and Van Alstine applied the Two Body Dirac
equations of constraint dynamics to the meson quark-antiquark bound states
using a relativistic extention of the Adler-Piran potential and compared their
spectral results to those from other approaches, ones which also considered
meson spectroscopy as a whole and not in parts. In this paper we explore in
more detail the differences and similarities in an important subset of those
approaches, the quasipotential approach. In the earlier paper, the
transformation properties of the quark-antiquark potentials were limited to a
scalar and an electromagnetic-like four vector, with the former accounting for
the confining aspects of the overall potential, and the latter the short range
portion. A part of that work consisted of developing a way in which the static
Adler-Piran potential was apportioned between those two different types of
potentials in addition to covariantization. Here we make a change in this
apportionment that leads to a substantial improvement in the resultant
spectroscopy by including a time-like confining vector potential over and above
the scalar confining one and the electromagnetic-like vector potential. Our fit
includes 19 more mesons than the earlier results and we modify the scalar
portion of the potential in such a way that allows this formalism to account
for the isoscalar mesons {\eta} and {\eta}' not included in the previous work.
Continuing the comparisons made in the previous paper with other approaches to
meson spectroscopy we examine in this paper the quasipotential approach of
Ebert, Faustov, and Galkin for a comparison with our formalism and spectral
results.Comment: Revisions of earlier versio
Kinematics and hydrodynamics of spinning particles
In the first part (Sections 1 and 2) of this paper --starting from the Pauli
current, in the ordinary tensorial language-- we obtain the decomposition of
the non-relativistic field velocity into two orthogonal parts: (i) the
"classical part, that is, the 3-velocity w = p/m OF the center-of-mass (CM),
and (ii) the so-called "quantum" part, that is, the 3-velocity V of the motion
IN the CM frame (namely, the internal "spin motion" or zitterbewegung). By
inserting such a complete, composite expression of the velocity into the
kinetic energy term of the non-relativistic classical (i.e., newtonian)
lagrangian, we straightforwardly get the appearance of the so-called "quantum
potential" associated, as it is known, with the Madelung fluid. This result
carries further evidence that the quantum behaviour of micro-systems can be
adirect consequence of the fundamental existence of spin. In the second part
(Sections 3 and 4), we fix our attention on the total 3-velocity v = w + V, it
being now necessary to pass to relativistic (classical) physics; and we show
that the proper time entering the definition of the four-velocity v^mu for
spinning particles has to be the proper time tau of the CM frame. Inserting the
correct Lorentz factor into the definition of v^mu leads to completely new
kinematical properties for v_mu v^mu. The important constraint p_mu v^mu = m,
identically true for scalar particles, but just assumed a priori in all
previous spinning particle theories, is herein derived in a self-consistent
way.Comment: LaTeX file; needs kapproc.st
Quantization from an exponential distribution of infinitesimal action
A statistical model of quantization based on an exponential distribution of
infinitesimal action is proposed. Trajectory which does not extremize the
action along an infinitesimal short segment of path is allowed to occur with a
very small probability following an exponential law. Planck constant is argued
to give the average deviation from the infinitesimal stationary action.Comment: 15 pages, accepted for publication in Physica
Time-like flows of energy-momentum and particle trajectories for the Klein-Gordon equation
The Klein-Gordon equation is interpreted in the de Broglie-Bohm manner as a
single-particle relativistic quantum mechanical equation that defines unique
time-like particle trajectories. The particle trajectories are determined by
the conserved flow of the intrinsic energy density which can be derived from
the specification of the Klein-Gordon energy-momentum tensor in an
Einstein-Riemann space. The approach is illustrated by application to the
simple single-particle phenomena associated with square potentials.Comment: 14 pages, 11 figure
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