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Quantum state smoothing is a technique for assigning a valid quantum state to a partially observed dynamical system, using measurement records both prior and posterior to an estimation time. We show that the technique is greatly simplified…
Quantum theory of field (extended) objects without a priori space-time geometry has been represented. Intrinsic coordinates in the tangent fibre bundle over complex projective Hilbert state space $CP(N-1)$ are used instead of space-time…
The wave-particle duality of the vacuum states of quantum fields is considered and the particle-like property of the vacuum state of a quantum field is proposed as a vacuum-particle which carries the vacuum-energy and the vacuum-momentum of…
We have developed a formalism that includes both quasibound states with real energies and quantum resonances within the same theoretical framework, and that admits a clean and unambiguous distinction between these states and the states of…
A recently proposed phase space condition which comprises information about the vacuum structure and timelike asymptotic behavior of physical states is verified in massless free field theory. There follow interesting conclusions about the…
Since symmetry properties of coherent states (CS) on M\"obius strip (MS) and fermions are closely related, CS on MS are naturally associated to the topological properties of fermionic fields. Here we consider CS and superpositions of…
In this paper, a characterization of maps between quantum states that preserve pure states and strict convex combinations is obtained. Based on this characterization, a structural theorem for maps between multipartite quantum states that…
Numerical simulation of individual open quantum systems has proven advantages over density operator computations. Quantum state diffusion with a moving basis (MQSD) provides a practical numerical simulation method which takes full advantage…
Quantum matter in quantum space-time is discussed using general properties of energy-conservation laws. As a rather radical conclusion, it is found that standard methods of differential geometry and quantum field theory on curved space-time…
We discuss various descriptions of a quantum particle on noncommutative space in a (possibly non-constant) magnetic field. We have tried to present the basic facts in a unified and synthetic manner, and to clarify the relationship between…
Quantum weak energy inequalities have recently been extensively discussed as a condition on the dynamical stability of quantum field states, particularly on curved spacetimes. We formulate the notion of a quantum weak energy inequality for…
We study the fuzzy spaces (as special examples of noncommutative manifolds) with their quasicoherent states in order to find their pertinent metrics. We show that they are naturally endowed with two natural "quantum metrics" which are…
The free scalar field is studied on the Y-junction of three semi infinite axes which is the simplest example of a non-manifold space. It is shown that under an assumption that the junction point can not gain a macroscopic amount of energy…
We point out that quantum field theories based on the concept of Clifford space and Clifford algebra valued-fields involve both positive and negative energies. This is a consequence of the indefinite signature (p,q) of the Clifford space.…
We investigate chains of 'd' dimensional quantum spins (qudits) on a line with generic nearest neighbor interactions without translational invariance. We find the conditions under which these systems are not frustrated, i.e. when the ground…
Bargmann invariants and null phase curves are known to be important ingredients in understanding the essential nature of the geometric phase in quantum mechanics. Null phase manifolds in quantum-mechanical ray spaces are submanifolds made…
Consider a symmetric quantum state on an n-fold product space, that is, the state is invariant under permutations of the n subsystems. We show that, conditioned on the outcomes of an informationally complete measurement applied to a number…
It is commonly assumed that quantum field theory arises by applying ordinary quantum mechanics to the low energy effective degrees of freedom of a more fundamental theory defined at ultra-high-energy/short-wavelength scales. We shall argue…
We investigate the construction of coherent states for quantum theories of connections based on graphs embedded in a spatial manifold, as in loop quantum gravity. We discuss the many subtleties of the construction, mainly related to the…
In the framework of quantum field theory in curved space-time, we study the quantization of a massless fermion field on a non-extremal Kerr black hole. The key theme in this note is the fundamental difference between scalar and fermion…