Related papers: Quantum mechanics not on manifold
The complex Hilbert space of standard quantum mechanics may be treated as a real Hilbert space. The pure states of the complex theory become mixed states in the real formulation. It is then possible to generalize standard quantum mechanics,…
A quantum field has been coupled to a space-time with accelerating expansion. Dynamical modes are destabilised successively at shorter material wavelengths as they metamorphose from oscillators to repellers. Due to degeneracy of energy…
We review some recent progress in quantum field theory in non-commutative space, focusing onto the fuzzy sphere as a non-perturbative regularisation scheme. We first introduce the basic formalism, and discuss the limits corresponding to…
The quantum three-wave interaction, the lowest order nonlinear interaction in plasma physics, describes energy-momentum transfer between three resonant waves in the quantum regime. We describe how it may also act as a…
We report briefly on an approach to quantum theory entirely based on symmetry grounds which improves Geometric Quantization in some respects and provides an alternative to the canonical framework. The present scheme, being typically…
We review aspects of classical and quantum mechanics of many anyons confined in an oscillator potential. The quantum mechanics of many anyons is complicated due to the occurrence of multivalued wavefunctions. Nevertheless there exists, for…
We consider a particle with a position-dependent mass, moving in a three-dimensional semi-infinite parallelepipedal or cylindrical channel under the influence of some hyperbolic potential. We show that the lack of uniformity in the…
A new approach to quantum gravity is presented based on a nonlinear quantization scheme for canonical field theories with an implicitly defined Hamiltonian. The constant mean curvature foliation is employed to eliminate the momentum…
In this review, we study some aspects of the non-equilibrium dynamics of quantum systems. In particular, we consider the effect of varying a parameter in the Hamiltonian of a quantum system which takes it across a quantum critical point or…
Quantum annealing (QA) is a promising approach for not only solving combinatorial optimization problems but also simulating quantum many-body systems such as those in condensed matter physics. However, non-adiabatic transitions constitute a…
We use a perturbative approach to evaluate transition amplitudes corresponding to quantum friction, for a scalar model describing an atom which moves at a constant velocity, close to a material plane. In particular, we present results on…
We study a model of quantum Yang-Mills theory with a finite number of gauge invariant degrees of freedom. The gauge field has only a finite number of degrees of freedom since we assume that space-time is a two dimensional cylinder. We…
Remarkably we find that for a ring with linear boundary conditions such that the eigenvector and its derivative are continuous, there does not seem to be a way for the well-known de Broglie relation to be gauge invariant. Certain nonlinear…
We show how quantum mechanics can be understood as a space-time theory provided that its spatial continuum is modelled by a variable real number (qrumber) continuum. Such a continuum can be constructed using only standard Hilbert space…
The concept of a particle is ambiguous in quantum field theory. It is generally agreed that particles depend not only on spacetime, but also on coordinates used to parametrise spacetime points. One of us has in contrast proposed a…
We give simple examples of weakly coupled or free quantum mechanical systems that exhibit scale invariance with an anomalous dimension for a conserved current. In these models scaling as an exact symmetry only emerges in a large N limit,…
We investigate the thermodynamical properties of quantum fields in curved spacetime. Our approach is to consider quantum fields in curved spacetime as a quantum system undergoing an out-of-equilibrium transformation. The non-equilibrium…
The scattering and bound states of the many-body systems, related to the short-range Dyson model, are studied. First, we show that the scattering states can be realized as coherent states and the scattering Hamiltonian can be connected to a…
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…
The quantum version of the free fall problem is a topic often skipped in undergraduate quantum mechanics courses because its discussion usually requires wavepackets built on the Airy functions -- a difficult computation. Here, on the…