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These are lecture notes for an introductory course on noncommutative field and gauge theory. We begin by reviewing quantum mechanics as the prototypical noncommutative theory, as well as the geometrical language of standard gauge theory.…
This article reviews some aspects of local covariance and of the ambiguities and anomalies involved in the definition of the stress energy tensor of quantum field theory in curved spacetime. Then, a summary is given of the approach proposed…
We investigate the vacuum and thermal fluctuations of a neutral massless scalar field living in Minkowski spacetime and interacting with a finite number of point-like obstacles, modelled by zero-range potentials. The system is described…
We develop an exact quantum thermodynamic description for a noninteracting nanoscale steady state that couples strongly with multiple reservoirs. It is demonstrated that there exists a steady-state extension of the thermodynamic function…
Our fundamental theories, i.e., the quantum theory and general relativity, are invariant under time reversal. Only when we treat system from the point of view of thermodynamics, i.e., averaging between many subsystem components, an arrow of…
The dependence of thermal field theory on the surface of quantization and on the velocity of the heat bath is investigated by working in general coordinates that are arbitrary linear combinations of the Minkowski coordinates. In the general…
We give an outlook on the future of coherence theory and many-body quantum dynamics as experiments develop in the arena of ultra-cold atoms. Novel results on quantum heating of center-of-mass temperature in evaporative cooling and…
Quantum systems of indistinguishable particles are commonly described using the formalism of second quantisation, which relies on the assumption that any admissible quantum state must be either symmetric or anti-symmetric under particle…
Noncommutative spacetimes are widely believed to model some properties of the quantum structure of spacetime at the Planck regime. In this contribution the construction of (anti-)de Sitter noncommutative spacetimes obtained through quantum…
We present a first numerical investigation of a non-commutative gauge theory defined via the spectral action for Moyal space with harmonic propagation. This action is approximated by finite matrices. Using Monte Carlo simulation we study…
Solving the time-dependent quantum many-body Schr\"odinger equation is a challenging task, especially for states at a finite temperature, where the environment affects the dynamics. Most existing approximating methods are designed to…
An equilibrium state can be represented by a pure quantum state, which we call a thermal pure quantum (TPQ) state. We propose a new TPQ state and a simple method of obtaining it. A single realization of the TPQ state suffices for…
It is well-known that thermal equilibrium states in quantum statistical mechanics and quantum field theory can be described in a mathematically rigorous manner by means of the so-called Kubo-Martin-Schwinger (KMS) condition, which is based…
The usual formulations of quantum field theory in Minkowski spacetime make crucial use of features--such as Poincare invariance and the existence of a preferred vacuum state--that are very special to Minkowski spacetime. In order to…
We elaborate further the functional Schr\"{o}dinger-picture approach to the quantum field in curved spacetimes using the generalized invariant method and construct explicitly the Fock space, which we relate with the thermal field theory. We…
Noncommutative space has been found to be of use in a number of different contexts. In particular, one may use noncommutative spacetime to generate quantised gravity theories. Via an identification between the Moyal $\star$-product on…
In this paper the connection between quantum field theories on flat noncommutative space(-times) in Euclidean and Lorentzian signature is studied for the case that time is still commutative. By making use of the algebraic framework of…
It is shown how quantum field theory at finite temperature can be used to set up self-consistent and gauge invariant equations for cosmological perturbations sustained by an ultrarelativistic plasma. While in the collisionless case, the…
Within the context of the twisted Poincar\'e algebra, there exists no noncommutative analogue of the Minkowski space interpreted as the homogeneous space of the Poincar\'e group quotiented by the Lorentz group. The usual definition of…
A new microcanonical equilibrium state is introduced for quantum systems with finite-dimensional state spaces. Equilibrium is characterised by a uniform distribution on a level surface of the expectation value of the Hamiltonian. The…