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The apparent impossibility of extending non-relativistic quantum mechanics to a relativistic quantum theory is shown to be due to the insufficient structural richness of the field of complex numbers over which quantum mechanics is built. A…
This article provides a cartoon of the quantization of General Relativity using the ideas of effective field theory. These ideas underpin the use of General Relativity as a theory from which precise predictions are possible, since they show…
I review some recent work where ideas and methods from Quantum Field Theory have proved useful in probability and vice versa. The topics discussed include the use of Renormalization Group theory in Stochastic Partial Differential Equations…
We consider decoupling in the context of an effective quantum field theory of two scalar fields with well separated mass scales and a $Z_2\times Z_2$ symmetry. We first prove, using Wilson's exact renormalization group equation, that the…
Physics beyond the standard model can affect top-quark physics indirectly. We describe the effective field theory approach to describing such physics, and contrast it with the vertex-function approach that has been pursued previously. We…
We study the renormalization of non-commutative gauge theories with matter. As in the scalar field theory cases, there are logarithmic infrared divergences resulting from integrating out high momentum modes. In order to reproduce the…
Using the Cartan formulation of General Relativity, we construct a well defined lattice-regularized theory capable to describe large non-perturbative quantum fluctuations of the frame field (or the metric) and of the spin connection. To…
We address the treatment of gauge theories within the framework that is formed from combining the machinery of noncommutative symplectic geometry, as introduced by Kontsevich, with Costello's approach to effective gauge field theories…
Starting from non-minimal supergravity theory with unified gauge symmetry, we obtain the low-energy effective theory by taking the flat limit and integrating out the superheavy fields in a model-independent manner. The scalar potential has…
In gauge theories, physical histories are represented by space-time connections modulo gauge transformations. The space of histories is thus intrinsically non-linear. The standard framework of constructive quantum field theory has to be…
These are expanded lecture notes of a mini-course whose objectives were to introduce the basic concepts, constructions and techniques of noncommutative geometry, as well as their uses as a framework for modelling quantum spacetime. Key…
New proves of decoupling of massive fields in several quantum field theories are derived in the effective Lagrangian approach based on Wilson renormalization group. In the most interesting case of gauge theories with spontaneous symmetry…
First, we briefly review the description of gravity theories as gauge theories in three and four dimensions. Specifically, we recall the procedure in which the results of General Relativity in three and four dimensions are recovered in a…
A nonlinear Wightman field is taken to be a nonlinear map from a linear space of test functions to a linear space of Hilbert space operators, with inessential modifications to other axioms only to the extent dictated by the introduction of…
Low-energy effective theories have been used very successfully to study the low-energy limit of QCD, providing us with results for a plethora of phenomena, ranging from bound-state formation to phase transitions in QCD. These theories are…
One of the obstacles to reconciling quantum theory with general relativity, is constructing a theory which is both consistent with observation, and and gives finite answers at high energy, so that the theory holds at arbitrarily short…
We develop a quantization scheme for the quantum theory of a real scalar field on a class of non-commutative spacetime models collectively known as T-Minkowski. Requiring the theory to be covariant under T-Poincar\'e transformations, we…
The quantum gravity is formulated based on gauge principle. The model discussed in this paper has local gravitational gauge symmetry and gravitational field is represented by gauge potential. A preliminary study on gravitational gauge group…
A general method to build the entanglement renormalization (cMERA) for interacting quantum field theories is presented. We improve upon the well-known Gaussian formalism used in free theories through a class of variational non-Gaussian…
We construct a gravity dual for scale invariant but non-conformal field theories with a cyclic renormalization group flow. A slight modification of our construction gives a gravity dual of discretely scale invariant field theories. The…