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Defining the Work Done on an Electromagnetic Field
摘要： The problem of defining work done on an electromagnetic field (EMF) via moving charges does not have a ready solution, because the standard Hamiltonian of an EMF—whose time derivative should define the work according to the first law—is not gauge invariant. This limits applications of statistical mechanics to an EMF. We obtained a new, explicitly gauge-invariant Hamiltonian for an EMF that depends only on physical observables. This Hamiltonian allows us to define work and to formulate the second law for an EMF. It also leads to a direct link between this law and the electrodynamic arrow of time, i.e., choosing retarded, and not advanced solutions of wave equations. Measuring the thermodynamic work can determine whether the photon mass is small but nonzero.
关键词： photon mass,work,second law,Hamiltonian,electromagnetic field,gauge invariance,electrodynamic arrow of time
更新于2025-09-23 15:19:57
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Gauge ambiguities imply Jaynes-Cummings physics remains valid in ultrastrong coupling QED
摘要： Ultrastrong-coupling between two-level systems and radiation is important for both fundamental and applied quantum electrodynamics (QED). Such regimes are identified by the breakdown of the rotating-wave approximation, which applied to the quantum Rabi model (QRM) yields the apparently less fundamental Jaynes-Cummings model (JCM). We show that when truncating the material system to two levels, each gauge gives a different description whose predictions vary significantly for ultrastrong-coupling. QRMs are obtained through specific gauge choices, but so too is a JCM without needing the rotating-wave approximation. Analysing a circuit QED setup, we find that this JCM provides more accurate predictions than the QRM for the ground state, and often for the first excited state as well. Thus, Jaynes-Cummings physics is not restricted to light-matter coupling below the ultrastrong limit. Among the many implications is that the system's ground state is not necessarily highly entangled, which is usually considered a hallmark of ultrastrong-coupling.
关键词： quantum Rabi model,circuit QED,gauge invariance,Jaynes-Cummings model,ultrastrong coupling,quantum electrodynamics
更新于2025-09-19 17:15:36
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On the canonical quantization of the electromagnetic field and the emergence of gauge invariance
摘要： In the framework of the canonical quantization of the electromagnetic (cid:12)eld, we impose as primary condition on the dynamics the positive de(cid:12)niteness of the energy spectrum. This implies that (Glauber) coherent states have to be considered for the longitudinal and the scalar photon (cid:12)elds. As a result we obtain that the relation holds which in the traditional approach is called the Gupta-Bleuler condition. Gauge invariance emerges as a property of the physical states. The group structure of the theory is recognized to be the one of SU (2)(cid:10)SU (1; 1).
关键词： coherent states,electromagnetic field,canonical quantization,gauge invariance,Gupta-Bleuler condition
更新于2025-09-10 09:29:36
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Gauge invariance and origin independence of electronic charge density and current density induced by optical fields
摘要： Expressions for the first-order polarization charge density ρ(1) and current density J(1) induced in a molecule by a monochromatic plane wave, obtained by time-dependent quantum mechanical perturbation theory, have been investigated to assess their gauge invariance and independence of the coordinate system in passive and active translations. The conditions arrived at show that, within the (long wavelengths) dipole approximation, only the electric contributions to these densities are needed to rationalize the phenomenology. To the next higher quadrupole approximation, assuming that the magnetic field and the electric field gradient are uniform over the molecular dimensions, corresponding contributions to ρ(1) and J(1) are considered. It has been found that total densities are independent of the origin, whereas the contributions from electric and magnetic fields are not separately invariant. A magnetic contribution to J(1), which is by itself origin independent, can be defined by means of an approach based on continuous translation of the origin of the coordinate system.
关键词： time-dependent perturbation theory,origin independence,quadrupole approximation,current density,optical fields,gauge invariance,dipole approximation,electronic charge density
更新于2025-09-09 09:28:46
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A gauge-invariant formulation of interband and intraband currents in solids
摘要： Experiments and simulations in solid-state high harmonic generation often make use of the distinction between interband and intraband currents. These two contributions to the total current have been associated with qualitatively different processes as well as physically measurable signatures, for example, in the spectral phase of harmonic emission. However, it was recently argued [P. F?ldi, Phys. Rev. B 96, 035112 (2017)] that these quantities can depend on the gauge employed in calculations. Since physical quantities are expected to have gauge-independent values, this raises the question of whether the decomposition of the total current into interband and intraband contributions is physically meaningful or merely a feature of a particular mathematical representation of nature. In this article, we explore this apparent ambiguity. We show that a closely related issue arises when calculating instantaneous band populations. In both the case of inter/intraband currents and the case of instantaneous band populations, we propose definitions that are gauge invariant and thus allow these quantities to be calculated consistently in any gauge.
关键词： gauge invariance,solid-state,interband currents,band populations,intraband currents,high harmonic generation
更新于2025-09-09 09:28:46
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Orbital Angular Momentum: How to Define it and How to Measure it
摘要： In the context of the controversy concerning the ambiguities in the definition of quark and gluon angular momentum we explain pedagogically the origin of these ambiguities and stress that there are fundamentally only three physically relevant variants. We give precise expressions for the sum rules involving them. We consider their measurement, both experimentally and on the lattice, and discuss some attempts to calculate them in models.
关键词： quark,gluon,QCD,gauge invariance,angular momentum
更新于2025-09-09 09:28:46