Search Results (10)

A consistent theory of quantum entanglement requires that constituent single-particle states belong to the same Hilbert space, the coherent eigenstates of a complete set of operators in a given representation, defined with respect to a shared continuous parameterization. Formulating such eigenstates for a single relativistic particle with spin, and applying them to the description of many-body states, presents well-known challenges. In this paper, we review the covariant theory of relativistic spin and entanglement in a framework first proposed by Stueckelberg and developed by Horwitz, Piron, et al. This approach modifies Wigner’s method by introducing an arbitrary timelike unit vector $n^{\mu }$ and then inducing a representation of $SL(2,C)$, based on $p^{\mu }$ rather than on the spacetime momentum. Generalizing this approach, we construct relativistic spin states on an extended phase space $\{(x^{\mu },p^{\mu }),({\zeta }^{\mu },{\pi }^{\mu })\}$, inducing a representation on the momentum ${\pi }^{\mu }$, thus providing a novel dynamical interpretation of the timelike unit vector $n^{\mu }={\pi }^{\mu }/M$. Studying the unitary representations of the Poincaré group on the extended phase space allows us to define basis quantities for quantum states and develop the gauge invariant electromagnetic Hamiltonian in classical and quantum mechanics. We write plane wave solutions for free particles and construct stable singlet states, and relate these to experiments involving temporal interference, analogous to the spatial interference known from double slit experiments. Full article

Within the realm of aging, the nexus between diet and health has garnered considerable attention. However, only select studies have amalgamated insights into the correlation between plant and animal food consumption and frailty. Our aim was to appraise the connections between the overall plant-based diet index (PDI), healthful plant-based diet index (hPDI), and unhealthful plant-based diet index (uPDI) and frailty in the elderly, utilizing data from the Chinese Longitudinal Healthy Longevity Survey (CLHLS). This cohort study drew upon CLHLS data spanning from 2008 to 2018. The PDI, hPDI, and uPDI were gauged using a simplified food frequency questionnaire (FFQ). A frailty index, encompassing 35 variables across major health domains, was formulated. Cox proportional hazard models were employed to scrutinize the associations between the three plant-based dietary indices and frailty in older adults, including an exploration of gender disparities in these associations. A cohort of 2883 study participants was encompassed, with 1987 (68.9%) observed to be either frail or in the pre-frail stage. The Cox model with penalized spline exhibited linear associations of PDI, hPDI, and uPDI with the frailty index. Following covariate adjustments, it was discerned that older adults situated in the highest quartiles of PDI (HR = 0.86, 95% CI: 0.77–0.95) and hPDI (HR = 0.83, 95% CI: 0.74–0.93) experienced a 14% and 17% diminished risk of frailty compared to those in the lowest quartiles of PDI and hPDI, respectively. Conversely, when contrasted with those in the lowest quartile of uPDI, older adults adhering to the highest tertile of uPDI exhibited a 21% elevated risk of frailty (HR = 1.21, 95% CI: 1.08–1.36), with both associations achieving statistical significance (p < 0.01). Moreover, additional subgroup analyses revealed that the protective effects of PDI and hPDI against frailty and the deleterious effects of uPDI were more conspicuous in men compared to women. To forestall or decelerate the progression of frailty in the elderly, tailored dietary interventions are imperative, particularly targeting male seniors. Full article

In this review, we revisit our latest works regarding the description of the gravitational interaction on noncommutative spaces as matrix models. Specifically, inspired by the gauge-theoretic approach of (ordinary) gravity, we make use of the suggested methodology, modified appropriately for the noncommutative framework, of the well-established formulation of gauge theories on them. Making use of a covariant four-dimensional fuzzy space, we formulate the gauge theory with an extended gauge group due to noncommutativity. In turn, in order to decrease the amount of symmetry we employ a symmetry breaking and result with an action which describes a theory that is a minimal noncommutative extension of the original. Full article

Using the path integral formulation in Euclidean space, we extended the calculation of the abelian chiral anomalies in the case of Lorentz violating theories by considering a new fermionic correction term provided by the standard model extension, which arises in the continuous Hamiltonian of a weakly tilted Weyl semimetal, and whose cones have opposite tilting. We found that this anomaly is insensitive to the tilting parameter, retaining its well-known covariant form. This independence on the Lorentz violating parameters is consistent with other findings reported in the literature. The initially imposed gauge invariant regularization was consistently recovered at the end of the calculation by the appearance of highly non-trivial combinations of the covariant derivatives, which ultimately managed to give only terms containing the electromagnetic tensor. We emphasize that the value of the anomaly with an arbitrary parameter is not automatically related to the effective action describing the electromagnetic response of such materials. Full article

We consider the problem of the choice of gauge in nonrelativistic strong-laser-field physics. For this purpose, we use the phase-space path-integral formalism to obtain the momentum-space matrix element of the exact time-evolution operator. With the assumption that the physical transition amplitude corresponds to transitions between eigenstates of the physical energy operator rather than the unperturbed Hamiltonian $H_0={(-i\partial /\partial \mathbf{r})}^2/2+V\left(\mathbf{r}\right)$, we prove that the aforementioned momentum-space matrix elements obtained in velocity gauge and length gauge are equal. These results are applied to laser-assisted electron-ion radiative recombination (LAR). The transition amplitude comes out identical in length gauge and velocity gauge, and the expression agrees with the one conventionally obtained in length gauge. In addition to the strong-field approximation (SFA), which is the zeroth-order term of our expansion, we present explicit results for the first-order and the second-order terms, which correspond to LAR preceded by single and double scattering, respectively. Our general conclusion is that in applications to atomic processes in strong-field physics the length-gauge version of the SFA (and its higher-order corrections) should be used. Using the energy operator as the basis-defining Hamiltonian, we have shown that the resulting transition amplitude is gauge invariant and agrees with the form commonly derived in length gauge. Full article

The canonical formulation of general relativity (GR) is based on decomposition space–time manifold M into $R\times \Sigma$ , where $R$ represents the time, and $\Sigma$ is the three-dimensional space-like surface. This decomposition has to preserve the invariance of GR, invariance under general coordinates, and local Lorentz transformations. These symmetries are associated with conserved currents that are coupled to gravity. These symmetries are studied on a three dimensional space-like hypersurface $\Sigma$ embedded in a four-dimensional space–time manifold. This implies continuous symmetries and conserved currents by Noether’s theorem on that surface. We construct a three-form $E_i\wedge D{A}^i$ (D represents covariant exterior derivative) in the phase space $(E_i^a,A_a^i)$ on the surface $\Sigma$ , and derive an equation of continuity on that surface, and search for canonical relations and a Lagrangian that correspond to the same equation of continuity according to the canonical field theory. We find that ${\Sigma }_i^{0a}$ is a conjugate momentum of $A_a^i$ and ${\Sigma }_i^{ab}{F}_{ab}^i$ is its energy density. We show that there is conserved spin current that couples to $A^i$ , and show that we have to include the term $F_{\mu \nu i}{F}^{\mu \nu i}$ in GR. Lagrangian, where $F^i=D{A}^i$ , and $A^i$ is complex $SO\left(3\right)$ connection. The term $F_{\mu \nu i}{F}^{\mu \nu i}$ includes one variable, $A^i$ , similar to Yang–Mills gauge theory. Finally we couple the connection $A^i$ to a left-handed spinor field $\psi$ , and find the corresponding beta function. Full article

A fully relativistically covariant and manifestly gauge-invariant formulation of classical Maxwell electrodynamics is presented, purely in terms of gauge-invariant potentials without entailing any gauge fixing. We show that the inhomogeneous equations satisfied by the physical scalar and vector potentials (originally discovered by Maxwell) have the same symmetry as the isometry of Minkowski spacetime, thereby reproducing Einstein’s incipient approach leading to his discovery of special relativity as a spacetime symmetry. To arrive at this conclusion, we show how the Maxwell equations for the potentials follow from stationary electromagnetism by replacing the Laplacian operator with the d’Alembertian operator, while making all variables dependent on space and time. We also establish consistency of these equations by deriving them from the standard Maxwell equations for the field strengths, showing that there is a unique projection operator which projects onto the physical potentials. Properties of the physical potentials are elaborated through their iterative Nöther coupling to a charged scalar field leading to the Abelian Higgs model, and through a sketch of the Aharonov–Bohm effect, where dependence of the Aharonov–Bohm phase on the physical vector potential is highlighted. Full article

The covariant formulation of teleparallel gravity theories must include the spin connection, which has 6 degrees of freedom. One can, however, always choose a gauge such that the spin connection is put to zero. In principle this gauge may affect counting of degrees of freedom in the Hamiltonian analysis. We show for general teleparallel theories of gravity, that fixing the gauge such that the spin connection vanishes in fact does not affect the counting of degrees of freedom. This manifests in the fact that the momenta of the Lorentz transformations which generate the spin connection are fully determined by the momenta of the tetrads. Full article

We review the recent progress in studying the quantum structure of $6D$ , $\mathcal{N}=(1,0)$ , and $\mathcal{N}=(1,1)$ supersymmetric gauge theories formulated through unconstrained harmonic superfields. The harmonic superfield approach allows one to carry out the quantization and calculations of the quantum corrections in a manifestly $\mathcal{N}=(1,0)$ supersymmetric way. The quantum effective action is constructed with the help of the background field method that secures the manifest gauge invariance of the results. Although the theories under consideration are not renormalizable, the extended supersymmetry essentially improves the ultraviolet behavior of the lowest-order loops. The $\mathcal{N}=(1,1)$ supersymmetric Yang–Mills theory turns out to be finite in the one-loop approximation in the minimal gauge. Furthermore, some two-loop divergences are shown to be absent in this theory. Analysis of the divergences is performed both in terms of harmonic supergraphs and by the manifestly gauge covariant superfield proper-time method. The finite one-loop leading low-energy effective action is calculated and analyzed. Furthermore, in the Abelian case, we discuss the gauge dependence of the quantum corrections and present its precise form for the one-loop divergent part of the effective action. Full article

We review the Lagrangian formulation of (generalised) Noether symmetries in the framework of Calculus of Variations in Jet Bundles, with a special attention to so-called “Natural Theories” and “Gauge-Natural Theories” that include all relevant Field Theories and physical applications (from Mechanics to General Relativity, to Gauge Theories, Supersymmetric Theories, Spinors, etc.). It is discussed how the use of Poincar´e–Cartan forms and decompositions of natural (or gauge-natural) variational operators give rise to notions such as “generators of Noether symmetries”, energy and reduced energy flow, Bianchi identities, weak and strong conservation laws, covariant conservation laws, Hamiltonian-like conservation laws (such as, e.g., so-calledADMlaws in General Relativity) with emphasis on the physical interpretation of the quantities calculated in specific cases (energy, angular momentum, entropy, etc.). A few substantially new and very recent applications/examples are presented to better show the power of the methods introduced: one in Classical Mechanics (definition of strong conservation laws in a frame-independent setting and a discussion on the way in which conserved quantities depend on the choice of an observer); one in Classical Field Theories (energy and entropy in General Relativity, in its standard formulation, in its spin-frame formulation, in its first order formulation “à la Palatini” and in its extensions to Non-Linear Gravity Theories); one in Quantum Field Theories (applications to conservation laws in Loop Quantum Gravity via spin connections and Barbero–Immirzi connections). Full article