Related papers: Prequantisation from the path integral viewpoint
Feynman path integrals are now a standard tool in quantum physics and their use in differential geometry leads to new mathematical insights. A logical treatment of quantum phenomena seems to require a sustained mathematical analysis of path…
We start to develop the quantization formalism in a hyperbolic Hilbert space. Generalizing Born's probability interpretation, we found that unitary transformations in such a Hilbert space represent a new class of transformations of…
Suppose we have two nonequivalent but s-equivalent Lagrange functions, the question arises: are they both equally well fitted for the Feynman quantization procedure or do they lead to two different quantization schemes.
We discuss path integrals for quantum mechanics with a potential which is a perturbation of the upside-down oscillator. We express the path integral (in the real time) by the Wiener measure. We obtain the Feynman integral for perturbations…
When employing Feynman path integrals to compute propagators in quantum physics, the concept of summing over the set of all paths is not always naive. In fact, an auxiliary phase often has to be included as a weight for each summand. In…
Modern cryptography is largely based on complexity assumptions, for example, the ubiquitous RSA is based on the supposed complexity of the prime factorization problem. Thus, it is of fundamental importance to understand how a quantum…
Quantum theory's irreducible empirical core is a probability calculus. While it presupposes the events to which (and on the basis of which) it serves to assign probabilities, and therefore cannot account for their occurrence, it has to be…
p-Adic generalization of the Feynman path integrals in quantum mechanics is considered. The probability amplitude for a particle in a constant field is calculated. Path integrals over p-adic space have the same form as those over R.
By using path integrals, the stochastic process associated to the time evolution of the quantum probability density is formally rewritten in terms of a stochastic differential equation, given by Newton's equation of motion with an…
Complexified Lienard-Wiechert potentials simplify the mathematics of Kerr-Newman particles. Here we constrain them by fiat to move along Bohmian trajectories to see if anything interesting occurs, as their equations of motion are not known.…
Heisenberg motion equations in Quantum mechanics can be put into the Hamilton form. The difference between the commutator and its principal part, the Poisson bracket, can be accounted for exactly. Canonical transformations in Quantum…
The Feynman parametrization of the Dirac equation is considered in order to obtain an indefinite mass formulation of relativistic quantum mechanics. It is shown that the parameter that labels the evolution is related to the proper time. The…
This paper proposes an approach of the unified consideration of classical and quantum mechanics from the standpoint of the complex analysis effects. It turns out that quantization can be interpreted in terms of the Riemann surface…
Both statistics and quantum theory deal with prediction using probability. We will show that there can be established a connection between these two areas. This will at the same time suggest a new, less formalistic way of looking upon basic…
In orthodox Standard Quantum Mechanics (SQM) bases and factorizations are considered to define quantum states and entanglement in relativistic terms. While the choice of a basis (interpreted as a measurement context) defines a state…
A covariant quantization scheme employing reducible representations of canonical commutation relations with positive-definite metric and Hermitian four-potentials is tested on the example of quantum electrodynamic fields produced by a…
Many quantization schemes rely on analogs of classical mechanics where the connections with classical mechanics are indirect. In this work I propose a new and direct connection between classical mechanics and quantum mechanics where the…
The de Broglie-Bohm interpretation of quantum mechanics and quantum field theory is generalized in such a way that it describes trajectories of relativistic fermionic particles and antiparticles and provides a causal description of the…
We investigate the non-perturbative quantization of phantom and ghost degrees of freedom by relating their representations in definite and indefinite inner product spaces. For a large class of potentials, we argue that the same physical…
Given an arbitrary Lagrangian function on \RR^d and a choice of classical path, one can try to define Feynman's path integral supported near the classical path as a formal power series parameterized by "Feynman diagrams," although these…