相关论文: Towards the Born-Weyl Quantization of Fields
Attempts for a geometrical interpretation of Quantum Theory were made, notably the deBroglie-Bohm formulation. This was further refined by Santamato who invoked Weyl's geometry. However these attempts left a number of unanswered questions.…
We review the status and present range of applications of the ``string-inspired'' approach to perturbative quantum field theory. This formalism offers the possibility of computing effective actions and S-matrix elements in a way which is…
For classical field theories with probabilistic initial conditions the classical field observables are an idealization. Their arbitrarily precise values poorly reflect the characteristic uncertainty in the presence of substantial…
The quantum theory of relativistic particles, based on the first quantization technique similar to that used by Schroedinger and Dirac in formulating quantum mechanics, is reconsidered on the basis of a photon-like dispersion relation…
We present a general classification of Hamiltonian multivector fields and of Poisson forms on the extended multiphase space appearing in the geometric formulation of first order classical field theories. This is a prerequisite for computing…
Nonrelativistic quantum mechanics and conformal quantum mechanics are deformed through a Jordanian twist. The deformed space coordinates satisfy the Snyder noncommutativity. The resulting deformed Hamiltonians are pseudo-Hermitian…
A quantum field theory approach is put forward to generalize the concept of classical spatial light beams carrying orbital angular momentum to the single-photon level. This quantization framework is carried out both in the paraxial and…
$C^*$-algebraic Weyl quantization is extended by allowing also degenerate pre-symplectic forms for the Weyl relations with infinitely many degrees of freedom, and by starting out from enlarged classical Poisson algebras. A powerful tool is…
A general formalism is developed that allows the construction of field theory on quantum spaces which are deformations of ordinary spacetime. The symmetry group of spacetime is replaced by a quantum group. This formalism is demonstrated for…
The Hamilton--Jacobi formalism generalized to 2--dimensional field theories according to Lepage's canonical framework is applied to several covariant real scalar fields, e.g. massless and massive Klein--Gordon, Sine--Gordon, Liouville and…
We perform, in a manifestly $SO(n-1,1)$ [$SO(n)$] covariant fashion, the Hamiltonian analysis of general relativity in $n$ dimensions written as a constrained $BF$ theory. We solve the constraint on the $B$ field in a way naturally adapted…
We develop a quantization scheme for the quantum theory of a real scalar field on a class of non-commutative spacetime models collectively known as T-Minkowski. Requiring the theory to be covariant under T-Poincar\'e transformations, we…
A Dirac picture perturbation theory is developed for the time evolution operator in classical dynamics in the spirit of the Schwinger-Feynman-Dyson perturbation expansion and detailed rules are derived for computations. Complexification…
Generalized Weyl quantization formalism for the cylindrical phase space $S^1 \times \mathbb{R}^1$ is developed. It is shown that the quantum observables relevant to the phase of linear harmonic oscillator or electromagnetic field can be…
The general method for treating non-Gaussian wave functionals in the Hamiltonian formulation of a quantum field theory, which was previously proposed and developed for Yang--Mills theory in Coulomb gauge, is generalized to full QCD. For…
It is the goal of this article to extend the notion of quantization from the standard interpretation focused on non-commuting observables defined starting from classical analogues, to the topological equivalents defined in terms of…
We discuss a covariant setting for Hamiltonian formalism in a relativistic field theory and we use this to obtain again the properties of Hamilton principal functional in Newtonian mechanics, relativistic mechanics, Klein-Gordon,…
In contrast with QFT, classical field theory can be formulated in a strict mathematical way if one defines even classical fields as sections of smooth fiber bundles. Formalism of jet manifolds provides the conventional language of dynamic…
Quantum theory of photons based on the first quantization technique, similar to that used by Schroedinger in the formulation of quantum mechanics, is considered. First, scalar quantum mechanics of photons operating with the photon wave…
Superconducting circuit quantisation conventionally starts from classical Euler-Lagrange circuit equations-of-motion. Invoking the correspondence principle yields a canonically quantised circuit description of circuit dynamics over a…