Related papers: A note on Gunningham's formula

This is the Ph.D. thesis of the author. In this thesis, we construct the $ P(\phi)_2 $ Quantum Field Theory (QFT) model on curved surfaces and show that it satisfies Segal's axioms (arXiv:2403.12804). An important ingredient in this…

We couple to group field theory (GFT) a scalar field that encodes the entanglement between manifold sites. The scalar field provides a relational clock that enables the derivation of the Hamiltonian of the system from the GFT action.…

We establish the spin-statistics theorem for topological quantum field theories (TQFTs) in the framework of Atiyah. We incorporate spin via spin structures on bordisms, and represent statistics using super vector spaces. Unitarity is…

We study Quot schemes of vector bundles on algebraic curves. Marian and Oprea gave a description of a topological quantum field theory (TQFT) studied by Witten in terms of intersection numbers on Quot schemes of trivial bundles. Since these…

In this paper, we present a construction toward a new type of TQFTs at the crossroads of low-dimensional topology, algebraic geometry, physics, and homotopy theory. It assigns TMF-modules to closed 3-manifolds and maps of TMF-modules to…

We present a general framework for TQFT and related constructions using the language of monoidal categories. We construct a topological category C and an algebraic category D, both monoidal, and a TQFT functor is then defined as a certain…

We present a rigorous quantization scheme that yields a quantum field theory in general boundary form starting from a linear field theory. Following a geometric quantization approach in the K\"ahler case, state spaces arise as spaces of…

Homotopy Quantum Field Theories (HQFTs) generalize more familiar Topological Quantum Field Theories (TQFTs). In generalization of the surgery construction of 3-dimensional TQFTs from modular categories, we use surgery to derive…

Using canonical quantisation, and eschewing the Schwinger-Keldysh path integral, we derive a version of the Worldline Quantum Field Theory (WQFT) formalism suitable for both scattering and bound configurations of the classical two-body…

The requirement of general covariance of quantum field theory (QFT) naturally leads to quantization based on the manifestly covariant De Donder-Weyl formalism. To recover the standard noncovariant formalism without violating covariance,…

Spinfoam models provide a covariant formulation of the dynamics of loop quantum gravity. They are non-perturbatively defined in the group field theory (GFT) framework: the GFT partition function defines the sum of spinfoam transition…

In this paper, we begin constructing a new finite-dimensional topological quantum field theory (TQFT) for three-manifolds, based on group PSL(2,C) and its action on a complex variable by fractional-linear transformations, by providing its…

We construct a 2nd quantized reformulation of canonical Loop Quantum Gravity at both kinematical and dynamical level, in terms of a Fock space of spin networks, and show in full generality that it leads directly to the Group Field Theory…

Quantum computers will work by evolving a high tensor power of a small (e.g. two) dimensional Hilbert space by local gates, which can be implemented by applying a local Hamiltonian H for a time t. In contrast to this quantum engineering,…

We introduce a formalism for constructing cohomological field theories (CohFT) out of nonlinear PDEs based on the first author's previous work (arXiv:2202.12425). We apply the formalism to the generalized Seiberg-Witten equations and show…

In this thesis, we study the structure of Group Field Theories (GFTs) from the point of view of renormalization theory. Such quantum field theories are found in approaches to quantum gravity related to Loop Quantum Gravity (LQG) on the one…

The paper puts together some loosely connected observations, old and new, on the concept of a quantum field and on the properties of Feynman amplitudes. We recall, in particular, the role of (exceptional) elementary induced representations…

For p>3 a prime, and g>2 an integer, we use Topological Quantum Field Theory (TQFT) to study a family of p-1 highest weight modules L_p(lambda) for the symplectic group Sp(2g,K) where K is an algebraically closed field of characteristic p.…

This Editorial introduces the Special Issue "Progress in Group Field Theory and Related Quantum Gravity Formalisms" which includes a number of research and review articles covering results in the group field theory (GFT) formalism for…

For a positive integer r, an r-spin topological quantum field theory is a 2-dimensional TQFT with tangential structure given by the r-fold cover of SO_2 . In particular, such a TQFT assigns a scalar invariant to every closed r-spin surface…