Related papers: Is Born-Jordan really the universal Path Integral …
Work belongs to the most basic notions in thermodynamics but it is not well understood in quantum systems, especially in open quantum systems. By introducing a novel concept of work functional along individual Feynman path, we invent a new…
The Hamilton-Jacobi method of constrained systems is discussed. The equations of motion of a singular system with time dependent constraints are obtained as total differential equations in many variables. The integrability conditions for…
We formulate Feynman path integral on a non commutative plane using coherent states. The propagator for a free particle exhibits UV cut-off induced by the parameter of non commutativity.
We express the unitary time evolution in non-relativistic regularized quantum electrodynamics at zero and positive temperature by a Feynman integral defined in terms of a complex Brownian motion. An average over the quantum electromagnetic…
A recent proposal to connect the loop quantization with the spin foam model for cosmology via the path integral is hereby adapted to the case of mechanical systems within the framework of the so called polymer quantum mechanics. The…
Feynman's Lagrangian path integral was an outgrowth of Dirac's vague surmise that Lagrangians have a role in quantum mechanics. Lagrangians implicitly incorporate Hamilton's first equation of motion, so their use contravenes the uncertainty…
Extension of Feynman's path integral to quantum mechanics of noncommuting spatial coordinates is considered. The corresponding formalism for noncommutative classical dynamics related to quadratic Lagrangians (Hamiltonians) is formulated.…
We consider the Klein-Gordon equation on a static spacetime and minimally coupled to a static electromagnetic potential. We show that it is essentially self-adjoint on $C_{\mathrm{c}}^\infty$. We discuss various distinguished inverses and…
We present a semiclassical analysis of the quantum propagator of a particle confined on one side by a steeply, monotonically rising potential. The models studied in detail have potentials proportional to $x^{\alpha}$ for $x>0$; the limit…
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…
Despite the importance of the path integral, there have been relatively few attempts to look to the Lagrangian for a more realistic framework that might underlie quantum theory. While such realism is not available for the standard path…
The path integral formulation in quantum mechanics corresponds to the first quantization since it is just to rewrite the quantum mechanical amplitude into many dimensional integrations over discretized coordinates $x_n$. However, the path…
In classical kinetic or kinetic-like models a particle free path distribution is exponensial, but this is more likely to be an exception than a rule. In this paper we derive a linear Boltzmann-like equation for a general free path…
While the Born rule is traditionally introduced as a separate postulate of quantum mechanics, we show it emerges naturally from a modified Schr\"odinger equation that includes "small-signal truncation". This parallels the way quantum…
Quantum dynamics simulations of reactive molecular processes are commonly performed in a low-dimensional space spanned by highly optimized reactive coordinates. Usually, these sets of reactive coordinates consist of non-linear coordinates.…
The quantum measure in area tensor Regge calculus can be constructed in such the way that it reduces to the Feynman path integral describing canonical quantisation if the continuous limit along any of the coordinates is taken. This…
The auxiliary rules of quantum mechanics have always included the Born rule that connects probability with square modulus. This need not be the case, for it is possible to introduce probability into the theory through probability current…
Quantification starts with sum and product rules that express combination and partition. These rules rest on elementary symmetries that have wide applicability, which explains why arithmetical adding up and splitting into proportions are…
A non-relativistic quantum mechanical theory is proposed that describes the universe as a continuum of worlds whose mutual interference gives rise to quantum phenomena. A logical framework is introduced to properly deal with propositions…
According to the Born rule, the probability density in quantum theory is determined by the square of the wave function. A generally accepted derivation of this rule has not yet been proposed. In the given work, a simple physical picture is…