Jarzynski’s nonequilibriumwork relation can be understood as the realization of the (hidden) timegenerator reciprocal symmetry satisfied for the conditional probability function. To show this, we introduce the reciprocal process where the classical probability theory is expressedwith real wave functions, and derive amathematical relation using the symmetry.We further discuss that the descriptio...

As explained in the official CMI problem description set out by Arthur Jaffe and Edward Witten, YangMills theory is a generalization of Maxwell’s theory of electromagnetism, in which the basic dynamical variable is a connection on a G-bundle over four-dimensional space-time. Its quantum version is the key ingredient in the Standard Model of the elementary particles and their interactions, and a...

Using the recently discovered connection between bosonization and duality transformations, we give an explicit path-integral representation for the bosonization of a massive fermion coupled to a U(1) gauge potential (such as electromagnetism) in d ≥ 2 space (D = d + 1 ≥ 3 spacetime) dimensions. We perform this integral explicitly in the limit of large fermion mass. We find that the bosonic theo...

This paper shows how gauge theoretic structures arise in a noncommutative calculus where the derivations are generated by commutators. These patterns include Hamilton’s equations, structure of Levi–Civita connection, and generalizations electromagnetism that related to theory with early work Hermann Weyl. The territory here explored is self-contained mathematically. It elementary, algebraic, su...

Abstract We develop some ideas about gauge symmetry in the context of Maxwell’s theory electromagnetism Hamiltonian formalism. One great benefit this formalism is that it pairs momentum and configurational degrees freedom, so a decomposition one side into subsets can be translated other. In case electromagnetism, enables us to pair freedom electric field with vector potential. Another algorithm...

A scattering process with gravitons as an intermediate state is investigated. To study such a scattering, the Gravitoelectromagnetism theory considered. It gravitational built on analogy between gravity and electromagnetism. The complete Lagrangian formulation of gravitoelectromagnetic includes interactions fermions photons that leads us to calculate their amplitudes cross sections. In this con...

After a preliminary discussion of the relevance of the field nature of grav-itation interaction, both for the fundamental interaction of particles and the topology of space time, a method is proposed to produce and detect a dynamical gravitational field, allowing the determination of the order of magnitude of its propagation velocity. From the actual point of view of the physicist the structure...

Unifying physics by describing a variety of interactions – or even all interactions – within a common framework has long been an alluring goal for physicists. One of the most ambitious attempts at unification was made in the 1910s by Gustav Mie. Mie aimed to derive electromagnetism, gravitation, and aspects of the emerging quantum theory from a single variational principle and a well-chosen Lag...

Vacuum polarization, a key prediction of quantum theory, can cause variety intriguing phenomena that be triggered by high-intensity laser pulses. The Heisenberg-Euler theory the vacuum supplements Maxwell's electromagnetism with nonlinear photon-photon interactions mediated fluctuations. This work presents numerical solver for leading weak-field corrections. present code implementation reaches ...