Related papers: Quantum Field Theory and Representation Theory: A …
Systematic use of the infinite-dimensional spin representation simplifies and rigorizes several questions in Quantum Field Theory. This representation permutes ``Gaussian'' elements in the fermion Fock space, and is necessarily projective:…
Quantum gravity was born as that branch of modern theoretical physics that tries to unify its guiding principles, i.e., quantum mechanics and general relativity. Nowadays it is providing new insight into the unification of all fundamental…
Quantum Field Theory (QFT) is the basis of some of the most fundamental theories in modern physics, but it is not an easy subject to learn. In the present article we intend to pave the way from quantum mechanics to QFT for students at early…
We present the case for a fundamentally discrete quantum spacetime and for Group Field Theories as a candidate consistent description of it, briefly reviewing the key properties of the GFT formalism. We then argue that the outstanding…
We present a method which enables one to construct isospectral objects, such as quantum graphs and drums. One aspect of the method is based on representation theory arguments which are shown and proved. The complementary part concerns…
In this paper we propose an algebraic formulation of group field theory and consider non-Fock representations based on coherent states. We show that we can construct representations with infinite number of degrees of freedom on compact base…
The aim of this paper is to survey some aspects of mapping class groups with focus on their finite dimensional representations arising in topological quantum field theory.
A theoretical scheme, based on a probabilistic generalization of the Hamilton's principle, is elaborated to obtain an unified description of more general dynamical behaviors determined both from a lagrangian function and by mechanisms not…
The representations of the observable algebra of a low dimensional quantum field theory form the objects of a braided tensor category. The search for gauge symmetry in the theory amounts to finding an algebra which has the same…
We explain that a bulk with arbitrary dimensions can be added to the space over which a quantum field theory is defined. This gives a TQFT such that its correlation functions in a slice are the same as those of the original quantum field…
We introduce the key ideas behind the group field theory approach to quantum gravity, and the basic elements of its formalism. We also briefly report on some recent results obtained in this approach, concerning both the mathematical…
There is debate as to whether quantum field theory is, at bottom, a quantum theory of fields or particles. One can take a field approach to the theory, using wave functionals over field configurations, or a particle approach, using wave…
We show that many well-known quantum field theories emerge as representations of a single $^\ast$-algebra. These include free quantum field theories in flat and curved space-times, lattice quantum field theories, Wightman quantum field…
The current form of quantum mechanics is very successful and is almost certainly correct. It is remarkable, however, that the entire structure-from the mass, spin and charge labels on particlelike states to antisymmetry to broken internal…
We develop a mathematical theory of quantization of multidimensional variational principles, and compare it with traditional constructions of quantum field theory. We conjecture that mathematical realization of quantum field theory axioms,…
The problem of background independent quantum gravity is the problem of defining a quantum field theory of matter and gravity in the absence of an underlying background geometry. Loop quantum gravity (LQG) is a promising proposal for…
Induced representations for quantum groups are defined starting from coisotropic quantum subgroups and their main properties are proved. When the coisotropic quantum subgroup has a suitably defined section such representations can be…
We review briefly a stream of ideas concerning the role of quantum groups as hidden symmetries in conformal field theories, paying particular attention to the field theoretical representations of quantum groups based on Coulomb gas methods.…
A mathematical framework for relativistic quantum field theory is constructed with natural symmetry $\mathsf{so}(2,3)= \mathsf{sp}(2,\mathbb{ R})$. In this framework gravity and electromagnetism unify as aspects of the geometry. The source…
The concept of discrepancy plays an important role in the study of uniformity properties of point sets. For sets of random points, the discrepancy is a random variable. We apply techniques from quantum field theory to translate the problem…