Related papers: Functional Integration on Constrained Function Spa…
The paper puts together some loosely connected observations, old and new, on the concept of a quantum field and on the properties of Feynman amplitudes. We recall, in particular, the role of (exceptional) elementary induced representations…
In this paper we study the integrals of fractional parts of given functions, and develop some new tools to understand the behaviour of prime differences. We demonstrate how simply some seemingly difficult conjectures related to prime…
The quantum mechanics formalism introduced new revolutionary concepts challenging our everyday perceptions. Arguably, quantum entanglement, which explains correlations that cannot be reproduced classically, is the most notable of them.…
In this work, we introduce a new generalized integral transform involving many potentially known or new transforms as special cases. Basic properties of the new integral transform, that investigated in this work, include the existence…
We uncover a combinatorial structure governing the differential equations satisfied by wavefunction coefficients of scalar fields with generic masses in de Sitter space. Using an integral representation of the massive mode functions, we…
We propose a new framework for integrating quantifiers with other logical connectives in a higher-categorical setting. Our method systematically incorporates key coherence conditions-including those akin to the Beck-Chevalley property-and…
We present a perturbation theory by extending a prescription due to Feynman for computing the probability density function for the random flight motion. The method can be applied to a wide variety of otherwise difficult circumstances. The…
It is wellknown that the Feynman kernel for the free particle on the half-line can be expressed as a sum over classical paths if we take the contribution from the reflected path into account. The minus sign for the reflected path needs to…
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…
We consider the problem of constrained motion along a conic path under a given external potential function. The model is described as a second-class system capturing the behavior of a certain class of specific quantum field theories. By…
Coherent states path integral formalism for the simplest quantum algebras, q-oscillator, SU_q(2) and SU_q(1,1) is introduced. In the classical limit canonical structure is derived with modified symplectic and Riemannian metric. Non-constant…
Constrained Hamiltonian description of the classical limit is utilized in order to derive consistent dynamical equations for hybrid quantum-classical systems. Starting with a compound quantum system in the Hamiltonian formulation conditions…
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…
A generalized Feynman-Kac formula based on the Wiener measure is presented. Within the setting of a quantum particle in an electromagnetic field it yields the standard Feynman-Kac formula for the corresponding Schr\"odinger semigroup. In…
The hypergeometric function method naturally provides the analytic expressions of scalar integrals from concerned Feynman diagrams in some connected regions of independent kinematic variables, also presents the systems of homogeneous linear…
The saddle points of a conventional Feynman path integral are not entangled, since they comprise a sequence of classical field configurations. We combine insights from field theory and tensor networks by constructing a Feynman path integral…
Recently a nice work about the understanding of one-loop integrals has been done in [1] using the tricks of the projective space language associated to their Feynman parametrization. We find this language is also very suitable to deal with…
The paper presents a new formula for the fractional integration, which generalizes the Riemann-Liouville and Hadamard fractional integrals into a single form, which when a parameter fixed at different values, produces the above integrals as…
This work addresses integrating probabilistic propositional logic constraints into the distribution encoded by a probabilistic circuit (PC). PCs are a class of tractable models that allow efficient computations (such as conditional and…
The role of differential equations in the process of calculating Feynman integrals is reviewed. An example of a diagram is given for which the method of differential equations was introduced, the properties of the inverse-mass-expansion…