Related papers: On defining the Hamiltonian beyond quantum theory
A quantum field theory is described which is a supersymmetric classical model. -- Supersymmetry generators of the system are used to split its Liouville operator into two contributions, with positive and negative spectrum, respectively. The…
The general problem of finding the ground state energy of lattice Hamiltonians is known to be very hard, even for a quantum computer. We show here that this is the case even for translationally invariant systems. We also show that a quantum…
For some time the York time parameter has been identified as a candidate for a physically meaningful time in cosmology. An associated Hamiltonian may be found by solving the Hamiltonian constraint for the momentum conjugate to the York time…
A broad range of quantum optimisation problems can be phrased as the question whether a specific system has a ground state at zero energy, i.e.\ whether its Hamiltonian is frustration free. Frustration-free Hamiltonians, in turn, play a…
To admit a canonically conjugate time operator, the Hamiltonian has to be a generator of translations (like the momentum operator generates translations in space), so its spectrum must be unbounded. But the Hamiltonian governing our world…
To date, quantum mechanics has proven to be our most successful theoretical model. However, it is still surrounded by a "mysterious halo" that can be summarized in a simple but challenging question: Why quantum phenomena are not understood…
Energy-time uncertainty plays an important role in quantum foundations and technologies, and it was even discussed by the founders of quantum mechanics. However, standard approaches (e.g., Robertson's uncertainty relation) do not apply to…
We propose the idea that not all energy is a source of gravity. We discuss the role of energy in the theory of gravitation and provide a formulation of gravity which takes into account the quantum nature of the source. We show that gravity…
A formula to calculate the quantum fluctuations of energy in small subsystems of a hot and relativistic gas is derived. We find an increase in fluctuations for subsystems of small sizes, but we agrees with the energy fluctuations in the…
We address the multiplicity of solutions to the time-energy canonical commutation relation for a given Hamiltonian. Specifically, we consider a particle spatially confined in a potential free interval, where it is known that two distinct…
Energy-momentum (and angular momentum) for the Metric-Affine Gravity theory is considered from a Hamiltonian perspective (linked with the Noether approach). The important roles of the Hamiltonian boundary term and the many choices involved…
A theory of transformation is presented for the diagonalization of a Hamiltonian that is quadratic in creation and annihilation operators or in coordinates and momenta. It is the systemization and theorization of Dirac and…
The quantum harmonic oscillator is one of the most fundamental objects in physics. We consider the case where it is extended to an arbitrary number modes and includes all possible terms that are bilinear in the annihilation and creation…
In the Bayesian approach to probability theory, probability quantifies a degree of belief for a single trial, without any a priori connection to limiting frequencies. In this paper we show that, despite being prescribed by a fundamental…
Under the assumption that every material object can ultimately be described by quantum theory, we ask how a probe system evolves in a device prepared and kept in a superposition state of values of its classical parameter. We find that,…
Starting from a new understanding of the vacuum energy problem based on the combination of the phase space regularization and the holographic bound, we argue that quantum gravity should be understood as gravitized quantum theory, that is,…
The aim of these notes is to elucidate some aspects of quantum field theory in curved spacetime, especially those relating to the notion of particles. A selection of issues relevant to wave-particle duality is given. The case of a generic…
Despite its enormous empirical success, the formalism of quantum theory still raises fundamental questions: why is nature described in terms of complex Hilbert spaces, and what modifications of it could we reasonably expect to find in some…
The variation of the energy for a gravitational system is directly defined from the Hamiltonian field equations of General Relativity. When the variation of the energy is written in a covariant form it splits into two (covariant)…
The concept of effective particles as degrees of freedom in a relativistic quantum field theory is defined using a non-perturbative renormalization group procedure for Hamiltonians. However, every candidate for a basic physical theory…