We discusses the efficient quantum-quasiclassical method developed by V.S. Melezhik with co-authors [1-4], which has been successfully applied to calculate various few-body processes and has made it possible to resolve a number of topical problems in atomic [1,3-5], mesoatomic [2], and nuclear physics [6]. In this approach, a few-body quantum problem is reduced to the simultaneous integration...
We build a systematic calculational method for the covariant expansion of the two-point heat kernel $\hat K(\tau|x,x')$ for generic minimal and non-minimal differential operators of any order. This is the expansion in powers of dimensional background field objects -- the coefficients of the operator and the corresponding spacetime and vector bundle curvatures, suitable in renormalization and...
We discuss thermalization process in the kinetic approximation in the presence of non--zero initial anomalous quantum expectation values on top of an initial non--plankian (non--thermal) level population. Namely we derive a system of ``kinetic'' equations for the level population and anomalous expectation values in four--dimensional massive scalar field theory with $\varphi^4$...
A review of the nonrelativistic quantum electrodynamics (NRQED) as applied to the bound state problem is given. The main corrections to nonrelativistic binding energies are derived, such as the relativistic Breit-Pauli Hamiltonian of the leading order ($m\alpha^4$), the radiative corrections of the leading order ($m\alpha^5$). Then it is shown how complex particles (hadrons) can be...
Anomaly inflow is a relation between anomalies in quantum field theory on a manifold and anomalies in effective theories on the boundary. Relevant examples of the anomalies are the parity anomaly (the η invariant) and the global chiral anomaly (the Index of a Dirac operator). We study the η-invariant of a Dirac operator on a manifold with boundary subject to local boundary conditions with the...
In an attempt toward a better understanding of the vacuum of QCD I propose a condensation of the tachyonic mode in SU(2). In the Savvidy vacuum, this mode is known to be unstable. In an approximation where the gluon fields are reduced to the tachyonic mode, which can be considered as a complex scalar field in (1+1)-dimensions, I apply the methods known from the Higgs model and finite...
The talk is devoted to an explicit cutoff regularization of the Green's function for a covariant Laplace operator. It is planned to give definitions, explain properties (spectral representation, homogenization, covariance), and formulate results for the case of the four-dimensional Yang-Mills theory.
Schwinger-Keldysh diagram technique is usually involved in the calculation of real-time in-in correlation functions. In the case of thermal state, one can analytically continue imaginary time Matsubara correlation functions to real times. However, not all real-time correlation functions can be obtained by such procedure. Moreover, the numerical analytic continuation is an ill-posed problem....
We present an off-shell formulation of ${\cal N}=2$ higher spin supermultiplets within the harmonic
superspace approach. Each supermultiplet is described by a triple of unconstrained harmonic analytic
gauge superfields, with the linearized action of some universal form. To the first order in gauge superfields,
we give their off-shell cubic couplings to ${\cal N}=2$ matter hypermultiplets...
Massless irreducible representations of the Poincaré group in the six-dimensional Minkowski space are studied.
It is shown that the finite spin representation is defined by two integer or half-integer numbers
while the infinite spin representation is defined by the real parameter and one integer or half-integer number.
Massless infinite spin irreducible representations in the space of the...
The resonant process of the creation of an ultrarelativistic electron–positron pair by two hard gamma quanta in a strong electromagnetic field with intensity up to $10^{27} W/cm^2$ (the Breit–Wheeler process modified by an external field) was theoretically studied. Under resonance conditions, the intermediate virtual electron (positron) in the external field comes on the mass shell. As a...
According to quantum electrodynamics, a strong electromagnetic field can make the vacuum state decay via the production of electron-positron pairs. This process is accompanied by the emission of soft photons and generation of higher-order harmonics. These two radiation channels are described within the leading order by vertex and tadpole Feynman diagrams. Here we evaluate and discuss both of...
In [1]-[5] we developed the theory of spinors on the basis of the superalgebraic representation. In it, spinor field operators are constructed from Grassmann densities in the momentum space and derivatives with respect to them. We have shown that generators of transformations that preserve the CAR algebra of spinor creation and annihilation operators are analogs of Dirac gamma matrices and can...
We investigate massive models of quantum field theory of scalar field in logarithmic dimensions in Euclidean space. The Schwinger-Dyson equation and non-trivial solution for mass are considered in the paper.
The Schwinger-Dyson equation has the form:
$$ D^{-1} = \Delta^{-1} - \Sigma $$
where $D$ is a full propagator, $\Delta$ is a bar propagator, $\Sigma$ is a self-energy operator.
In...
We present a basis of eigenvectors for the graph building operators of planar fishnet Feynman integrals in d-dimensions. The eigenvectors are constructed with a set of creation/annihilation operators that satisfy the corresponding Zamolodchikovs-Faddeev algebra.
The spectral decomposition of a fishnet integral
we achieved can be applied to the computation of
Basso-Dixon integrals in...
A convenient integral representation for zig-zag four-point and
two-point planar Feynman diagrams relevant to the bi-scalar
D-dimensional fishnet field theory is obtained. This representation gives a possibility to evaluate exactly diagrams of the zig-zag series in special cases. In particular, we give a fairly simple proof of the Broadhurst-Kreimer conjecture about the values of zig-zag...
It has been shown that non-Abelian vortex string supported in four dimensional (4D) ${\mathcal N}=2$ supersymmetric QCD (SQCD) with the U(2) gauge group and $N_f = 4$ quark flavors becomes a critical superstring. This string propagates in the ten dimensional space formed by a product of the flat 4D space and an internal space given by a Calabi-Yau non-compact threefold, namely, the conifold....
