Related papers: Evolution of hybrid quantum-classical wavefunction…
The gauge invariant formulation of Maxwell's equations and the electromagnetic duality transformations are given in the light-front (LF) variables. The novel formulation of the LF canonical quantization, which is based on the kinematic…
Consistent interactions that can be added to a free, Abelian gauge theory comprising a BF model and a finite set of massless real scalar fields are constructed from the deformation of the solution to the master equation based on specific…
Gauge invariance was discovered in the development of classical electromagnetism and was required when the latter was formulated in terms of the scalar and vector potentials. It is now considered to be a fundamental principle of nature,…
Standard practice attempts to remove coordinate influence in physics through the use of invariant equations. Trans-coordinate physics proceeds differently by not introducing space-time coordinates in the first place. Differentials taken…
A class of high-order canonical symplectic structure-preserving geometric algorithms are developed for high-quality simulations of the quantized Dirac-Maxwell theory based strong-field quantum electrodynamics (SFQED) and relativistic…
The gauge covariant derivative of a wave function is ubiquitous in gauge theory, and with associated gauge transformations it defines charged currents interacting with external fields, such as the Lorentz force exerted by an electromagnetic…
Consistent dynamics which couples classical and quantum degrees of freedom exists, provided it is stochastic. This dynamics is linear in the hybrid state, completely positive and trace preserving. One application of this is to study the…
In earlier papers on the loop variable approach to gauge invariant interactions in string theory, a ``wave functional'' with some specific properties was invoked. It had the purpose of converting the generalized momenta to space time…
A non-perturbative quantum field theory of General Relativity is presented which leads to a new realization of the theory of Covariant Quantum-Gravity (CQG-theory). The treatment is founded on the recently-identified Hamiltonian structure…
In the case of a quantum-classical hybrid system with a finite number of degrees of freedom, the problem of characterizing the most general dynamical semigroup is solved, under the restriction of being quasi-free. This is a generalization…
The choice of mathematical representation when describing physical systems is of great consequence, and this choice is usually determined by the properties of the problem at hand. Here we examine the little-known wave operator…
Covariant classical particle dynamics is described, and the associated covariant relativistic particle quantum mechanics is derived. The invariant symmetric bracket is defined on the space of quantum amplitudes, and its relation to a…
Consistent dynamics which couples classical and quantum degrees of freedom exists. This dynamics is linear in the hybrid state, completely positive and trace preserving. Starting from completely positive classical-quantum master equations,…
The mathematical logic of a true nature of mirror symmetry expresses, in the case of the Dirac Lagrangian, the ideas of the left- and right-handed photons referring to long- and short-lived particles, respectively. Such a difference in…
The finite-temperature effective potential customarily employed to describe the physics of cosmological phase transitions often relies on specific gauge choices, and is manifestly not gauge-invariant at finite order in its perturbative…
We demonstrate the existence of a complex Hilbert Space with Hermitian operators for calculations in \textit{classical} electromagnetism that parallels the Hilbert Space of quantum mechanics. The axioms of this classical theory are the…
Biconformal spaces contain the essential elements of quantum mechanics, making the independent imposition of quantization unnecessary. Based on three postulates characterizing motion and measurement in biconformal geometry, we derive…
In the covariant canonical approach to classical physics, each point in phase space represents an entire classical trajectory. Initial data at a fixed time serve as coordinates for this ``timeless'' phase space, and time evolution can be…
A variational scheme for the derivation of generalized, symmetry-induced continuity equations for Hermitian and non-Hermitian quantum mechanical systems is developed. We introduce a Lagrangian which involves two complex wave fields and…
In this paper, we show that the Laughlin wave function is a Hamiltonian and its associated Berry connection as the Schr\"odinger equation by transforming the Schr\"odinger equation into the Kirchhoff equation which describes the evolution…