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The kinematical and dynamical symmetries of equations describing the time evolution of quantum systems like the supersymmetric harmonic oscillator in one space dimension and the interaction of a non-relativistic spin one-half particle in a…
A recursive algebraic method which allows to obtain the Feynman or Schwinger parametric representation of a generic L-loops and (E+1) external lines diagram, in a scalar $\phi ^{3}\oplus \phi ^{4}$ theory, is presented. The representation…
We introduce an efficient configuration space technique which allows one to compute a class of Feynman diagrams which generalize the scalar sunset topology to any number of massive internal lines. General tensor vertex structures and…
We describe an efficient practical procedure for enumerating and regrouping vacuum Feynman graphs of a given order in perturbation theory. The method is based on a combination of Schwinger-Dyson equations and the two-particle-irreducible…
We present a method to implement 3-dimensional N = 1 SUSY Yang-Mills theory (a theory with two real supercharges containing gauge fields and an adjoint Majorana fermion) on the lattice, including a way to implement the Chern-Simons term…
We present a four-dimensional (4D) ${\cal N}=1$ superfield description of supersymmetric Yang-Mills (SYM) theory in ten-dimensional (10D) spacetime with certain magnetic fluxes in compactified extra dimensions preserving partial ${\cal…
We consider the harmonic-superspace formalism in the $N=4$ supersymmetry using the $SU(4)/SU(2)\times SU(2)\times U(1)$ harmonics which was earlier applied to the abelian gauge theory. The N=4 non-abelian constraints in a standard…
We construct quantized free superfields and represent them as operator-valued distributions in Fock space starting with Majorana fields. The perturbative construction of the S-matrix for interacting theories is carried through by extending…
We consider two-dimensional N=(2,2) supersymmetric gauge theory on discretized Riemann surfaces. We find that the discretized theory can be efficiently described by using graph theory, where the bosonic and fermionic fields are regarded as…
We study the multipoint super-correlation functions of the full non-chiral stress-tensor multiplet in N=4 super-Yang-Mills theory in the Born approximation. We derive effective supergraph Feynman rules for them. Surprisingly, the Feynman…
On the basis of a new method to derive the effective action the nonperturbative concept of "dynamical generation" is explained. A non-trivial, non-Hermitian and PT-symmetric solution for Wightman's scalar field theory in four dimensions is…
We review a recently proposed SuperGeometric (SG) approach to Quantum Field Theories (QFTs) that allow for scalar-fermion field transformations in a manifestly reparameterisation covariant manner. By adopting natural choices for the…
An effective action is obtained for the $N=1$, $2D-$induced supergravity on a compact super Riemann surface (without boundary) $\hat\Sigma$ of genus $g>1$, as the general solution of the corresponding superconformal Ward identity. This is…
It is advocated that the superembedding approach is a generic covariant method for the description of superbranes as models of (partial) spontaneous supersymmetry breaking. As an illustration we construct (in the framework of…
We propose to include gravity in quantum field theory non-perturbatively, by modifying the propagators so that each virtual particle in a Feynman graph move in the space-time determined by the four-momenta of the other particles in the same…
We consider the field theory on non-commutative superspace and non-commutative spacetime that arises on D-branes in Type II superstring theory with a constant self-dual graviphoton and NS-NS $B$ field background. $\N=1$ supersymmetric field…
Feynman's diagrammatic series is a common language for a formally exact theoretical description of systems of infinitely-many interacting quantum particles, as well as a foundation for precision computational techniques. Here we introduce a…
New algebraic approach to analytical calculations of D-dimensional integrals for multi-loop Feynman diagrams is proposed. We show that the known analytical methods of evaluation of multi-loop Feynman integrals, such as integration by parts…
The answers for Feynman diagrams satisfy various kinds of differential equations -- which is not a surprise, because they are defined as Gaussian correlators, possessing a vast variety of Ward identities and superintegrability properties.…
A momentum-space approach to conformal field theory offers a new perspective on cosmological correlators and better reveals the underlying connections to scattering amplitudes. This thesis explores the interplay between integral…