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Quantum field theory is assumed to be gauge invariant. However it is well known that when certain quantities are calculated using perturbation theory the results are not gauge invariant. The non-gauge invariant terms have to be removed in…
In this article we give a totally new proof of the integral localization formula for equivariantly closed differential forms (Theorem 7.11 in [BGV]). We restate it here as Theorem 2. This localization formula is very well known, but the…
The Lagrange-mesh method is a very accurate procedure to compute eigenvalues and eigenfunctions of a two-body quantum equation. The method requires only the evaluation of the potential at some mesh points in the configuration space. It is…
The purpose of this paper is to present a Lagrangian from which we can derive the quantionic field equation written in the Dirac gauge using the principle of stationary action.
Quantum mechanics with a generalized uncertainty principle arises through a representation of the commutator $[\hat{x}, \hat{p}] = i f(\hat{p})$. We apply this deformed quantization to free scalar field theory for $f_\pm =1\pm \beta p^2$.…
A general dynamical invariant operator for three coupled time-dependent oscillators is derived. Although the obtained invariant operator satisfies the Liouville-von Neumann equation, its mathematical formula is somewhat complicated due to…
We develop a mathematical theory of quantization of multidimensional variational principles, and compare it with traditional constructions of quantum field theory. We conjecture that mathematical realization of quantum field theory axioms,…
We give new proofs of some well-known results from Invariant Theorey using the Kempf-Ness theorem.
In this paper, we consider a q-analogue of Laplace transform and we investigate some properties of q-Laplace transform. From our investigation, we derive some interesting formulae related to q-Laplace transform.
The Universal Field Equations, recently constructed as examples of higher dimensional dynamical systems which admit an infinity of inequivalent Lagrangians are shown to be linearised by a Legendre transformation. This establishes the…
We study fractional variational problems in terms of a generalized fractional integral with Lagrangians depending on classical derivatives, generalized fractional integrals and derivatives. We obtain necessary optimality conditions for the…
The status of multifractional theories is reviewed using comparative tables. Theoretical foundations, classical matter and gravity dynamics, cosmology and experimental constraints are summarized and the application of the multifractional…
Gauge invariant regularization of quantum field theory in the framework of Light-Front (LF) Hamiltonian formalism via introducing a lattice in transverse coordinates and imposing boundary conditions in LF coordinate $x^-$ for gauge fields…
Quantum field theory is assumed to be gauge invariant. It is shown that for a Dirac field the assumption of gauge invariance impacts on the way the vacuum state is defined. It is shown that the conventional definition of the vacuum state…
Based on certain assumptions for the expectation value of a product of the quantum fluctuating metric at two points, the gravitational and scalar field Lagrangians are evaluated. Assuming a vanishing expectation value of the first order…
In this paper, we prove a version of Lagrange's theorem for gyrogroups and use this result to prove that gyrogroups of particular orders have the strong Cauchy property.
In this paper, we develop an elementary proof of the change of variables in multiple integrals. Our proof is based on an induction argument. Assuming the formula for (m-1)-integrals, we define the integral over hypersurface in Rm, establish…
The most important problem of fundamental Physics is the quantization of the gravitational field. A main difficulty is the lack of available experimental tests that discriminate among the theories proposed to quantize gravity. Recently,…
The classical Landau-Lifshitz-Gilbert (LLG) equation has long served as a cornerstone for modeling magnetization dynamics in magnetic systems, yet its classical nature limits its applicability to inherently quantum phenomena such as…
Let $G$ be a Lie group, $\g$ its Lie algebra, and $U_h(\g)$ the corresponding quantum group. We consider some examples of $U_h(\g)$-invariant one and two parameter quantizations on $G$-manifolds.