Related papers: The Faddeev-Popov Method Demystified
Discrete analogs of the classical Kontorovich-Lebedev transforms are introduced and investigated. It involves series with the modified Bessel function or Macdonald function $K_{in}(x), x >0, n \in \mathbb{N}, i $ is the imaginary unit, and…
We present a simple field transformation which changes the field arguments from the ordinary position-space coordinates to the oblique phase-space coordinates that are linear in position and momentum variables. This is useful in studying…
We clarify and extend insights from Lavrentiev's seminal paper. We examine the original theorem dealing with the absence of the Lavrentiev phenomenon, a cornerstone issue in the calculus of variations. We point out some inconsistencies in…
An analysis about the antisymmetric tensor matter fields Avdeev-Chizhov theory in a curved space-time is performed. We show, in a curved spacetime, that the Avdeev-Chizhov theory can be seen as a kind of a $\lambda\phi^{4}$ theory for a…
In this work I show that a simple Field Theory on a non trivial gauge background may behave as a phantom field and contribute to an effective $w<-1$ state equation fluid contribution to cosmology.
The standard way to construct a path integral is to use a Legendre transformation to find the hamiltonian, to repeatedly insert complete sets of states into the time-evolution operator, and then to integrate over the momenta. This procedure…
The act of describing how a physical process changes a system is the basis for understanding observed phenomena. For quantum-mechanical processes in particular, the affect of processes on quantum states profoundly advances our knowledge of…
A simple mathematical extension of quantum theory is presented. As well as opening the possibility of alternative methods of calculation, the additional formalism implies a new physical interpretation of the standard theory by providing a…
In this paper, we introduced the theory of the sieve function transformation. Using the principle of sieve function transformation, we improved sieve method, and obtained the difference range of similar sieve function values. For this, we…
In this work is discussed possibility and actuality of Lagrangian approach to quantum computations. Finite-dimensional Hilbert spaces used in this area provide some challenge for such consideration. The model discussed here can be…
For the Legendre-Stirling numbers of the second kind asymptotic formulae are derived in terms of a local central limit theorem. Thereby, supplements of the recently published asymptotic analysis of the Chebyshev-Stirling numbers are…
We unveil the dynamical equivalence of field theories with non-canonical kinetic terms and canonical theories with a volume element invariant under transverse diffeomorphisms. The proof of the equivalence also reveals a subtle connection…
We study properties of a scalar quantum field theory on the two-dimensional noncommutative plane with $E_q(2)$ quantum symmetry. We start from the consideration of a firstly quantized quantum particle on the noncommutative plane. Then we…
A preferred form for the path integral discretization is suggested that allows the implementation of canonical transformations in quantum theory.
We show how to transform a $d$-dimensional Euclidean path integral in terms of two (Cartesian) fields to a path integral in terms of polar field variables. First we present a conjecture that states how this transformation should be done.…
The spectral density method being applied to the quantum field theory at finite temperature is revived and its possibilities are briefly discussed.
We employ the familiar canonical quantization procedure in a given cosmological setting to argue that it is equivalent to and results in the same physical picture if one considers the deformation of the phase-space instead. To show this we…
In this course we give a selfcontained introduction to the quantum field theory for trapped atomic gases, using functional methods throughout. We consider both equilibrium and nonequilibrium phenomena. In the equilibrium case, we first…
These two lectures give a pedagogical introduction to the ``string-inspired'' worldline technique for perturbative calculations in quantum field theory. This includes an overview over the present range of its applications. Several examples…
We study the application of formal diffeomorphisms to scalar fields. We give a new proof that interacting tree amplitudes vanish in the resulting theories. Our proof is directly at the diagrammatic level, not appealing to the path integral,…