Schrödinger equation in a general curved spacetime geometry

In this paper, we consider relativistic quantum field theory in the presence of an external electric potential in a general curved spacetime geometry. We utilize Fermi coordinates adapted to the time-like geodesic to describe the low-energy physics in the laboratory and calculate the leading correction due to the curvature of the spacetime geometry to the Schrödinger equation. We then compute the nonvanishing probability of excitation for a hydrogen atom that falls in or is scattered by a general Schwarzschild black hole. The photon emitted from the excited state by spontaneous emission extracts energy from the black hole, increases the decay rate of the black hole and adds to the information paradox.

Fundamental Spacetime Representations of Quantum Antenna Systems

We develop foundations for the emerging field of quantum antennas using relativistic quantum field theory. We show that the concept of "antenna" goes beyond electromagnetic waves. Any quantum radiation can be treated within quantum antenna theory, not only electromagnetic or acoustic radiation that dominated the field so far.

Fundamental Spacetime Representations of Quantum Antenna Systems

We develop foundations for the emerging field of quantum antennas using relativistic quantum field theory. We show that the concept of "antenna" goes beyond electromagnetic waves. Any quantum radiation can be treated within quantum antenna theory, not only electromagnetic or acoustic radiation that dominated the field so far.

Super-Macdonald Polynomials: Orthogonality and Hilbert Space Interpretation

The super-Macdonald polynomials, introduced by Sergeev and Veselov (Commun Math Phys 288: 653–675, 2009), generalise the Macdonald polynomials to (arbitrary numbers of) two kinds of variables, and they are eigenfunctions of the deformed Macdonald–Ruijsenaars operators introduced by the same authors in Sergeev and Veselov (Commun Math Phys 245: 249–278, 2004). We introduce a Hermitian form on the algebra spanned by the super-Macdonald polynomials, prove their orthogonality, compute their (quadratic) norms explicitly, and establish a corresponding Hilbert space interpretation of the super-Macdonald polynomials and deformed Macdonald–Ruijsenaars operators. This allows for a quantum mechanical interpretation of the models defined by the deformed Macdonald–Ruijsenaars operators. Motivated by recent results in the nonrelativistic ($$q\rightarrow 1$$ q → 1 ) case, we propose that these models describe the particles and anti-particles of an underlying relativistic quantum field theory, thus providing a natural generalisation of the trigonometric Ruijsenaars model.

Modular zero modes and sewing the states of QFT

We point out an important difference between continuum relativistic quantum field theory (QFT) and lattice models with dramatic consequences for the theory of multi-partite entanglement. On a lattice given a collection of density matrices ρ(1), ρ(2), ⋯, ρ(n) there is no guarantee that there exists an n-partite pure state |Ω〉12⋯n that reduces to these marginals. The state |Ω〉12⋯n exists only if the eigenvalues of the density matrices ρ(i) satisfy certain polygon inequalities. We show that in QFT, as opposed to lattice systems, splitting the space into n non-overlapping regions any collection of local states ω(1), ω(2), ⋯ ω(n) come from the restriction of a global pure state. The reason is that rotating any local state ω(i) by unitary Ui localized in the ith region we come arbitrarily close to any other local state ψ(i). We construct explicit examples of such local unitaries using the cocycle.

Wigner–Weyl formalism for the lattice models

We discuss application of Wigner–Weyl formalism to the lattice models of condensed matter physics and relativistic quantum field theory. For the noninteracting models our technique relates Wigner transformation of the fermionic Green’s function with the Weyl symbol [Formula: see text] of lattice Dirac operator. We take as an example of the model defined on rectangular lattice the model of Wilson fermions. It represents the regularization of relativistic quantum field theory and, in addition, describes qualitatively certain topological materials in condensed matter physics. In this model we derive expression for [Formula: see text] in the presence of the most general case of external [Formula: see text] gauge field. Next, we solve the Groenewold equation to all orders in powers of the derivatives of [Formula: see text].