We discuss the limits of the photon wavefunction (PWF) formalism, which is experiencing a revival in these days from the new practical applications in photonics and quantum optics. We build a Dirac-like equation for the PWF written in a manifestly covariant form and show that, in presence of charged matter fields, it reproduces the standard formulation of (classical) Electrodinamics. This shows the inconsistency of the attempts to construct a quantum theory of interacting photons, based on the so called photon wavefunction approach, alternative to standard QED. PWF formalism can then be used to provide an easier description of the propagation of free photons, when the photon number remains fixed in time.
We start from the QED Lagrangian to describe a charged many-particle system coupled to the radiation field. A covariant density matrix approach to kinetic theory of QED plasmas, subjected to a strong external electro-magnetic field has recently been developed [1,2]. We use the hyperplane formalism in order to perform a manifest covariant quantization and to implement initial correlations to the solution of the Liouville-von Neumann equation. A perturbative expansion in orders of the fine structure constant for the correlation functions as well as the statistical operator is applied. The non-eq…
The Schrödinger equation relates the electron wavefunction and the electric potential, which are emergent physical quantities. At that emergent level, the Schrödinger equation is either postulated as a principle of quantum physics or obtained heuristically. However, the Schrödinger equation is a low energy condition we can derive from the foundations of QED. Due to the small value of the electromagnetic coupling constant, we show that, in low energy interactions, the electric potential accurately represents the contributions of the intermediate photon exchanges. Then, we see that the dominant …
In quantum field theory it is generally assumed that there is a lower bound to the energy of a quantum state. Here, it will be shown that there is no lower bound to the energy of physical states in QED in a manifestly covariant gauge.
We develop a covariant density matrix approach to kinetic theory of QED plasmas subjected into a strong external electromagnetic field. A canonical quantization of the system on space-like hyperplanes in Minkowski space and a covariant generalization of the Coulomb gauge is used. The condensate mode associated with the mean electromagnetic field is separated from the photon degrees of freedom by a time-dependent unitary transformation of both, the dynamical variables and the nonequilibrium statistical operator. Therefore even in the case of strong external fields a perturbative expansion in or…
The earlier treatments of Lorentz covariant harmonic oscillator have brought to light various difficulties, such as reconciling Lorentz symmetry with the full Fock space, and divergence issues with their functional representations. We present here a full solution avoiding those problems. The complete set of Fock states is obtained, together with the corresponding explicit wavefunction and their inner product integrals free from any divergence problem and the Lorentz symmetry fully maintained without additional constraints imposed. By a simple choice of the pseudo-unitary representation of the …
We investigate the multiphoton states generated by high-gain optical parametric amplification of a single injected photon, polarization encoded as a ''qubit''. The experiment configuration exploits the optimal phase-covariant cloning in the high gain regime. The interference fringe pattern showing the non local transfer of coherence between the injected qubit and the mesoscopic amplified output field involving up to 4000 photons has been investigated. A probabilistic new method to extract full information about the multiparticle output wavefunction has been implemented.
Do the wavepacket-size of free-electron wavefunction and its history have physical effect in its interaction with light? Here we answer this problem by analyzing a QED model, considering both spontaneous and stimulated emission of quantized radiation field. For coherent radiation (Glauber state), we confirm that stimulated emission/absorption of photons has a dependence on wavepacket size that decays when it exceeds the interacting radiation wavelength, consistently and complementarily with Schrodinger equation analysis of wavepacket acceleration in classical electromagnetic field. Furthermore…
We propose, as an alternative theory of quantum mechanics, a relativistically covariant variational principle (VP) capable of describing both wavefunction collapse and, as an appropriate limiting case, evolution of the wavefunction according to the standard quantum mechanical (SQM) wave equation. This results in a nonlinear, nonlocal, time-symmetric hidden-variable theory; the hidden variable is the phase of the wavefunction, which affects the dynamics via zitterbewegung. The VP is δ(A_1 + εA_2) = 0, in which A_1 and A_2 are positive definite integrals (over all spacetime) of functions of the …
We attempt to pull together various lines of research whose ultimate conclusion points to the actual ``locality'' of Quantum Mechanics (QM). We note that just as John Bell discovered various errors in previous ``proofs'' of the completeness of QM, he made an error of his own in deriving the ``non-locality'' of QM. We show that QM satisfies the correct locality bound for non-commuting variables -- and is therefore local for 2 or more particles. We further show that the entangled wavefunctions that produce non-local de-Broglie-Bohm guidance equations are an artifact of First Quantization, and th…
In Bell inequality tests, the evolution of the wavefunction is not covariant, i.e. not invariant under velocity boost that change the time ordering of events, but the laws that govern the probability distribution of possible results are. In this note I investigate what this could mean and whether there could be some covariant "real quantum stuff". This clarifies the implication of the Free Will Theorem and of relativistic spontaneous localization models based on the flash ontology (rGRWf). Some implications for the concept of time(s) are spelled out.
We propose a fibre bundle formulation of the mathematical base of relativistic quantum mechanics. At the present stage the bundle form of the theory is equivalent to its conventional one, but it admits new types of generalizations in different directions. In the present, second, part of our investigation, we consider a covariant approach to bundle description of relativistic quantum mechanics. In it the wavefunctions are replaced with (state) sections of a suitably chosen vector bundle over space-time whose (standard) fibre is the space of the wavefunctions. Now the quantum evolution is descri…
Investigation of near field of QED requires the refuse from an averaging of the Lorentz condition that smooths out some field peculiarities. Instead of it Schwinger decomposition of the 4-potential with the Bogoliubov method of interaction switching in time and in space regions is considered. At such approach near field is describable by the part of covariant Green function of QED, the fast-damping Schwinger function formed by longitudinal and scalar components of Aμ none restricted by light cone. This description reveals possibility of superluminal phenomena within the near field zone as…
Subradiant excited states in finite chains of two-level quantum emitters coupled to a one-dimensional reservoir are a resource for superior photon storage and controlled photon manipulation. Typically, states storing multiple excitations exhibit fermionic correlations and are thus characterized by an anti-symmetric wavefunction, which makes them hard to prepare experimentally. Here we identify a class of quasi-localized dark states with up to half of the qubits excited, which appear for lattice constants that are an integer multiple of the guided-mode wavelength. They allow for a high-fidelity…
Modern advances in transformation optics and electromagnetic metamaterials made possible experimental demonstrations of highly unusual curvilinear optical spaces, such as various geometries necessary for electromagnetic cloaking. Recently we demonstrated that mapping light intensity in a hyperbolic metamaterial may also model the flow of time in an effective (2+1) dimensional Minkowski spacetime. Curving such an effective spacetime creates experimental model of a toy big bang. Here we demonstrate that at low light levels this model may be used to emulate a fully covariant version of quantum me…
Time-independent gauge transformations are implemented in the canonical formalism by the Gauss law which is not covariant. The covariant form of Gauss law is conceptually important for studying asymptotic properties of the gauge fields. For QED in $3+1$ dimensions, we have developed a formalism for treating the equations of motion (EOM) themselves as constraints, that is, constraints on states using Peierls' quantization. They generate spacetime dependent gauge transformations. We extend these results to the Maxwell-Chern-Simons (MCS) Lagrangian. The surprising result is that the covariant Gau…
We present in the article the formulation of a version of Lorentz covariant quantum mechanics based on a group theoretical construction from a Heisenberg-Weyl symmetry with position and momentum operators transforming as Minkowski four-vectors under the Lorentz symmetry. The basic representation is identified as a coherent state representation, essentially an irreducible component of the regular representation, with the matching representation of an extension of the group $C^*$-algebra giving the algebra of observables. The key feature of the formulation is that it is not unitary but pseudo-un…
In recent years simulations of chemistry and condensed materials has emerged as one of the preeminent applications of quantum computing, offering an exponential speedup for the solution of the electronic structure for certain strongly correlated electronic systems. To date, most treatments have ignored the question of whether relativistic effects, which are described most generally by quantum electrodynamics (QED), can also be simulated on a quantum computer in polynomial time. Here we show that effective QED, which is equivalent to QED to second order in perturbation theory, can be simulated …
Classical mechanics, relativity, electrodynamics and quantum mechanics are often depicted as separate realms of physics, each with its own formalism and notion. This remains unsatisfactory with respect to the unity of nature and to the necessary number of postulates. We uncover the intrinsic connection of these areas of physics and describe them using a common symplectic Hamiltonian formalism. Our approach is based on a proper distinction between variables and constants, i.e. on a basic but rigorous ontology of time. We link these concept with the obvious conditions for the possibility of meas…
