Related papers: Lorentz Invariant Renormalization in Causal Pertur…
We study various corrections of correlation functions to leading order in conformal perturbation theory, both on the cylinder and on the plane. Many problems on the cylinder are mathematically equivalent to those in the plane if we give the…
Translational invariance requires that physical predictions are independent of the choice of spatial coordinate system used. The time dilatation effect of special relativity is shown to manifestly respect this invariance. Consideration of…
It is known that some cosmological perturbations are conformal invariant. This facilitates the studies of perturbations within some gravitational theories alternative to general relativity, for example the scalar-tensor theory, because it…
The Epstein--Glaser type T-subtraction introduced by one of the authors in a previous paper is extended to the Lorentz invariant framework. The advantage of using our subtraction instead of Epstein and Glaser's standard W-subtraction method…
We construct the general renormalizable actions for the scalar field and the gauge field at a Lifshitz point characterized by the dynamical critical exponent $z$. The Lorentz invariance is broken down in the UV region, but is recovered in…
Perturbation theory can be reformulated as dynamical theory. Then a sequence of perturbative approximations is bijective to a trajectory of dynamical system with discrete time, called the approximation cascade. Here we concentrate our…
Renormalization procedure is generalized to be applicable for non renormalizable theories. It is shown that introduction of an extra expansion parameter allows to get rid of divergences and express physical quantities as series of finite…
Lorentz violation frequently induces modified dispersion relations that can yield space-like states that impede the standard quantization procedures. In certain cases, an extended hamiltonian formalism can be used to define…
In 3+1 space-time dimensions, fourth order derivative gravity is perturbatively renormalizable. Here it is shown that it describes a unitary theory of gravitons (with/without an additional scalar) in a limited coupling parameter space which…
Admitting the validity of Lorentz transformations for the space as time coordinates of the same event we derive their differential form in order to underline the correct prerequisites for the application of time and length contraction or…
We present a new approach to cosmological perturbations based on the theory of Lie groups and their representations. After re-deriving the standard covariant formalism from SO(3) considerations, we provide a new expansion of the perturbed…
We investigate to what extent renormalization can be understood as an algebraic manipulation on concatenated one-loop integrals. We find that the resulting algebra indicates a useful connection to knot theory.
Renormalization group in the internal space consists of the gradual change of the coupling constants. Functional evolution equations corresponding to the change of the mass or the coupling constant are presented in the framework of a scalar…
The parity violation at the level of weak interactions and other similar discrete symmetries breaking show that the invariance of laws under the full group of Lorentz transformations can not be taken granted. We examine the principle of…
Based only on simple principles of renormalization in coordinate space, we derive closed renormalized amplitudes and renormalization group constants at 1- and 2-loop orders for scalar field theories in general backgrounds. This is achieved…
We revisit and clarify some aspects of perturbative renormalization in pure Chern-Simons theory by means of a localization principle associated with an underlying supersymmetry. This perspective allows the otherwise perturbative one-loop…
A causal set is a partially ordered set on a countably infinite ground-set such that each element is above finitely many others. A natural extension of a causal set is an enumeration of its elements which respects the order. We bring…
We show that starting with the fact that special relativity theory is concerned with a distortion of the observed length of a moving rod, without mentioning if it is a "contraction" or "dilation", we can derive the Lorentz transformations…
We work on some general extensions of the formalism for theories which preserve the relativity of inertial frames with a nonlinear action of the Lorentz transformations on momentum space. Relativistic particle models invariant under the…
Time-reversal symmetry is a prevalent feature of microscopic physics, including operational quantum theory and classical general relativity. Previous works have studied indefinite causal structure using the language of operational quantum…