Related papers: Quantum Field Theory on Fock Projective Space
We discuss the second quantization of scalar field theory on the q-deformed fuzzy sphere S^2_{q,N} for q \in \R, using a path-integral approach. We find quantum field theories which are manifestly covariant under U_q(su(2)), have a smooth…
Studying a quantum field theory involves a choice of space-time manifold and a choice of background for any global symmetries of the theory. We argue that many more choices are possible when specifying the background. In the context of…
A proof is given for the Fourier transform for functions in a quantum mechanical Hilbert space on a non-compact manifold in general relativity. In the (configuration space) Newton-Wigner representation we discuss the spectral decomposition…
Regularization of quantum field theories (QFT's) can be achieved by quantizing the underlying manifold (spacetime or spatial slice) thereby replacing it by a non-commutative matrix model or a ``fuzzy manifold'' . Such discretization by…
These are notes on some entanglement properties of quantum field theory, aiming to make accessible a variety of ideas that are known in the literature. The main goal is to explain how to deal with entanglement when -- as in quantum field…
We argue that duality symmetries can be manifestly realised when theories with these symmetries are quantised using phase space quantum theory. In particular, using background fields and phase space quantum theory, we quantise the bosonic…
Quantization of the free Maxwell field in Minkowski space is carried out using a loop representation and shown to be equivalent to the standard Fock quantization. Because it is based on coherent state methods, this framework may be useful…
Variational Monte Carlo calculations have recently reached state-of-the-art accuracy in the approximation of ground state properties of quantum many-body systems. Making use of flexible neural quantum states and automatic differentiation…
An algebraic formalism for the study of a system of charged particles interacting with an external quantum field is developed. The notion of monoidal categories with duality is used for the description of composite systems and corresponding…
A theory of principal bundles possessing quantum structure groups and classical base manifolds is presented. Structural analysis of such quantum principal bundles is performed. A differential calculus is constructed, combining differential…
In a companion paper we studied field theory in the presence of a physical observer with quantum dynamics. Here we describe the most striking consequence of this assumption: new gauge and diff anomalies arise. The relevant cocycles depend…
The second quantization of M(atrix) theory in the free (Boltzmannian) Fock space is considered. It provides a possible framework to the recent Susskind proposal that U(N) supersymmetic Yang-Mills theories for all N might be embedded in a…
We consider quantum theory of fields \phi defined on a D dimensional manifold (bulk) with an interaction V(\phi) concentrated on a d<D dimensional surface (brane). Such a quantum field theory can be less singular than the one in d…
A characteristical property of a classical physical theory is that the observables are real functions taking an exact outcome on every (pure) state; in a quantum theory, at the contrary, a given observable on a given state can take several…
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…
I revisit the Wigner (or Weyl-Wigner, WW) representation of the quantum electromagnetic field. I show that, assuming that Fock states are just mathematical concepts devoid of physical reality, WW suggests a realistic interpretation which…
We study rainbow (fold) and cusp catastrophes that form in Fock space following a quench in a Bose Josephson junction. In the Gross-Pitaevskii mean-field theory the rainbows are singular caustics, but in the second-quantized theory a…
We give a mathematical definition of quantum field theory on a manifold, and definition of quantization of a classical field theory given by a variational principle.
We construct bosonic and fermionic locally covariant quantum field theories on curved backgrounds for large classes of fields. We investigate the quantum field and n-point functions induced by suitable states.
A collapse-free version of quantum theory is examined to systematically study the role of the projection postulate. This foil theory assumes "passive" measurements that do not update quantum states although measurement outcomes still occur…