Related papers: Quantum field theories with boundaries and novel i…
The basic problem of quantum cosmology is the definition of the quantum state of the universe, with appropriate boundary conditions on Riemannian three-geometries. This paper describes recent progress in the corresponding analysis of…
We present here a set of lecture notes on quantum systems with time-dependent boundaries. In particular, we analyze the dynamics of a non-relativistic particle in a bounded domain of physical space, when the boundaries are moving or…
If the block universe view is correct, the future and the past have similar status and one would expect physical theories to involve final as well as initial boundary conditions. A plausible consistency condition between the initial and…
Invariance principles determine many key properties in quantum field theory, including, in particular, the appropriate form of the boundary conditions. A crucial consistency check is the proof that the resulting boundary-value problem is…
Quantum theory on manifolds with boundaries have been studied extensively through von Neumann analysis of self adjoint operators. We approach the issues through introduction of singular $\delta$ and $\delta'$ potentials. The advantages of…
Quantum magnets represent an ideal playground for the controlled realization of novel quantum phases and of quantum phase transitions. The Hamiltonian of the system can be indeed manipulated by applying a magnetic field or pressure on the…
Quantum phase transitions are sudden changes in the ground-state wavefunction of a many-body system that can occur as a control parameter such as a concentration or a field strength is varied. They are driven purely by the competition…
It is well known that boundary conditions on quantum fields produce divergences in the renormalized energy-momentum tensor near the boundaries. Although irrelevant for the computation of Casimir forces between different bodies, the…
This study targets quantum phases which are characterized by topological properties and no associated with the symmetry breaking. We concern ourselves primarily with the transitions among these quantum phases. This type of quantum phase…
The most important recent results in the theory of phase transitions and quantum effects in quantum anharmonic crystals are presented and discussed. In particular, necessary and sufficient conditions for a phase transition to occur at some…
The fundamental laws of physics can be derived from the requirement of invariance under suitable classes of transformations on the one hand, and from the need for a well-posed mathematical theory on the other hand. As a part of this…
Boundary conditions in relativistic QFT can be classified by deep results in the theory of braided or modular tensor categories.
We study the behaviour of quantum field theories defined on a surface $S$ as it tends to a null surface $S_n$. In the case of a real, free scalar field theory the above limiting procedure reduces the system to one with a finite number of…
A quantum scalar field theory with spacetime-dependent coupling is studied. Surprisingly, while translation invariance is explicitly broken in the classical theory, momentum conservation is recovered at the quantum level for some specific…
Quantum field theory (QFT) on non-stationary spacetimes is well understood from the side of the algebra of observables. The state space, however, is largely unexplored, due to the non-existence of distinguished states (vacuum, scattering…
It is well known that (possibly non-unique) suitable field dynamics can be prescribed in spacetimes with timelike boundaries by means of appropriate boundary conditions. In Ref. [J. Math. Phys. {\bf 21}, 2802 (1980)], Wald derived a…
I propose to formalize quantum theories as topological quantum field theories in a generalized sense, associating state spaces with boundaries of arbitrary (and possibly finite) regions of space-time. I further propose to obtain such…
Over the past five years, there has been significant progress on the problem of quantization of diffeomorphism covariant field theories with {\it local} degrees of freedom. The absence of a background space-time metric in these theories…
A noncommutative geometric generalisation of the quantum field theoretical framework is developed by generalising the Heisenberg commutation relations. There appear nonzero minimal uncertainties in positions and in momenta. As the main…
The relation between connections on 2-dimensional manifolds and holomorphic bundles provides a new perspective on the role of classical gauge fields in quantum field theory in two, three and four dimensions. In particular we show that there…