Related papers: Improved Epstein-Glaser Renormalization II. Lorent…
We consider Rota-Baxter algebras of meromorphic forms with poles along a (singular) hypersurface in a smooth projective variety and the associated Birkhoff factorization for algebra homomorphisms from a commutative Hopf algebra. In the case…
We consider Carroll-invariant limits of Lorentz-invariant field theories. We show that just as in the case of electromagnetism, there are two inequivalent limits, one "electric" and the other "magnetic". Each can be obtained from the…
We show that the instabilities of higher derivative gravity models with quadratic curvature invariant $\alpha R^2+\beta R_{\mu\nu}R^{\mu\nu}$ can be removed by judicious addition of constraints at the quadratic level of metric fluctuations…
In special relativity, spacetime algebra (STA) provides a powerful and insightful approach to an invariant formulation of physics. However, in this geometric algebra of spacetime, relativistic physics is usually considered a misnomer: STA…
We generalize the coset construction of Callan, Coleman, Wess and Zumino to theories in which the Lorentz group is spontaneously broken down to one of its subgroups. This allows us to write down the most general low-energy effective…
We provide a unified geometric realization of the classical deformation complexes. We construct GL-equivariant bilinear incidence varieties whose diagonal slices recover the varieties of associative, commutative, Leibniz, and Lie algebra…
Asymmetric heterotic orbifolds are discussed from the worldsheet perspective. Starting from Buscher's gauging of a theory of D compact bosons the duality covariant description of Tseytlin is obtained after a non-Lorentz invariant gauge…
The unique Nature of the Lorentz group in four dimensions is the root cause of the many remarkable properties of the Einstein spacetimes, in particular their operational structure on the 2-forms. We show how this operational structure can…
The renormalization of general gauge theories on flat and curved space-time backgrounds is considered within the Sp(2)-covariant quantization method. We assume the existence of a gauge-invariant and diffeomorphism invariant regularization.…
The general, linear equations with constant coefficients on quantum Minkowski spaces are considered and the explicit formulae for their conserved currents are given. The proposed procedure can be simplified for *-invariant equations. The…
We observe that the replacement of the Riemann curvature with the generalized Riemann curvature into the corrections to the type II supergravity at order $\alpha'^3$ which are in terms of the contractions of four Riemann curvatures $R^4$,…
The subject of the thesis is the construction of a perturbative quantum theory of interacting fields on a curved space-time, following a point of view pioneered by Stueckelberg and Bogoliubov and developed by Epstein-Glaser on the flat…
We retreat the well-known Einstein-Cartan theory by slightly modifying the covariant derivative of spinor field by investigating double cover of the Lorentz group. We first write the Lagrangian consisting of the Einstein-Hilbert term, Dirac…
We introduce the "partial-$p$" operation in a massive Euclidean $\lambda\phi^{4}$ scalar field theory describing anisotropic Lifshitz critical behavior. We then develop a minimal subtraction a la $Bogoliubov-Parasyuk-Hepp-Zimmermann$…
The paper is another step towards a realisation of the goal, advanced in articles 1706.05682 [hep-th] and 1808.04470 [hep-th], of a systematic supersymmetry-equivariant geometrisation of physically distinguished Green-Schwarz…
We introduce a generalized framework for sampling and reconstruction in separable Hilbert spaces. Specifically, we establish that it is always possible to stably reconstruct a vector in an arbitrary Riesz basis from sufficiently many of its…
We study supersymmetric extension of the Einstein-aether gravitational model where local Lorentz invariance is broken down to the subgroup of spatial rotations by a vacuum expectation value of a timelike vector field called aether.…
Quantum gravity is analyzed from the viewpoint of the renormalization group. The analysis is based on methods introduced by J. Polchinski concerning the perturbative renormalization with flow equations. In the first part of this work, the…
The Lorentz covariant theory of propagation of light in the (weak) gravitational fields of N-body systems consisting of arbitrarily moving point-like bodies with constant masses is constructed. The theory is based on the Lienard-Wiechert…
We give an alternative method to obtain normal forms of reversible equivariant vector fields. We adapt the classical method using tools from invariant theory to establish formulae that take symmetries into account as a starting point.…