Narrow Results

The Weyl algebra — the usual C*-algebra employed to model the canonical commutation relations (CCRs), has a well-known defect, in that it has a large number of representations which are not regular and these cannot model physical fields. Here, we construct explicitly a C*-algebra which can reproduce the CCRs of a countably dimensional symplectic space (S, B) and such that its representation set is exactly the full set of regular representations of the CCRs. This construction uses Blackadar's version of infinite tensor products of nonunital C*-algebras, and it produces a "host algebra" (i.e. a generalized group algebra, explained below) for the σ-representation theory of the Abelian group S where σ(·,·) ≔ e^iB(·,·)/2. As an easy application, it then follows that for every regular representation of on a separable Hilbert space, there is a direct integral decomposition of it into irreducible regular representations (a known result).

We consider a family of irreducible Weyl representations of canonical commutation relations with infinite degrees of freedom on the abstract boson Fock space over a complex Hilbert space. Theorems on equivalence or inequivalence of the representations are established. As a simple application of one of these theorems, the well-known inequivalence of the time-zero field and conjugate momentum for different masses in a quantum scalar field theory is rederived with space dimension $d\ge 1$ arbitrary. Also a generalization of representations of the time-zero field and conjugate momentum is presented. Comparison is made with a quantum scalar field in a bounded region in ${ℝ}^d$. It is shown that, in the case of a bounded space region with $d=1,2,3$, the representations for different masses turn out to be mutually equivalent.

In de Sitter ambient space formalism, the massless minimally coupled scalar field can be constructed from a massless conformally coupled scalar field and a constant five-vector $A^{\alpha }$. Also, a constant five-vector $B^{\alpha }$ appears in the interaction Lagrangian of massless minimally coupled scalar and spinor fields in this formalism. These constant five-vector fields can be fixed in the interaction case in the null curvature limit. Here, we will calculate the ${𝒮}$ matrix elements of scalar–spinor field interaction in the tree level approximation. Then the constant five-vectors $A^{\alpha }$ and $B^{\alpha }$, will be fixed by comparing the ${𝒮}$ matrix elements in the null curvature limits with the Minkowskian counterparts.

We proposed Atomic Schwinger–Dyson method (ASD method) in previous paper, which was a nonperturbative and relativistic quantum field theory for a finite baryon density. We think it is important to show the significance of renormarization in order to get real physical predictions. Moreover, the real value of physical mass, electric charge and wave function are completely different from those of the non-renormalized electron and photon in mean field theory, since there are many of the particle-antiparticle creations and annihilations, particle-hole excitation, and Pauli blocking, which give an effect on bare mass, electric charge, polarization of vacuum, and self-energy. In this paper, we shows that ASD method is renormalizable theory, and that photon condensation of ASD method gave rise to Coulomb's potential and the mass shift of electron. The interacting photon and electron fields, which have physical mass and electric charge, are expressed as generalized free field equations by using the mass shift and the self-energy of those particles. We obtain the expression of an exact solution of these particles on the basis of the Green functional method.

We address the quantum estimation of parameters encoded into the initial state of two modes of a Dirac field described by relatively accelerated parties. By using the quantum Fisher information (QFI), we investigate how the weak measurements performed before and after the accelerating observer, affect the optimal estimation of information encoded into the weight and phase parameters of the initial state shared between the parties. Studying the QFI, associated with weight parameter $𝜗$, we find that the acceleration at which the optimal estimation occurs may be controlled by weak measurements. Moreover, it is shown that the post-measurement plays the role of a quantum key for manifestation of the Unruh effect. On the other hand, investigating the phase estimation optimization and assuming that there is no control over the initial state, we show that the weak measurements may be utilized to match the optimal $𝜗$ to its predetermined value. Moreover, in addition to determination of a lower bound on the QFI with the local quantum uncertainty (LQU), we unveil an important upper bound on the precision of phase estimation in our relativistic scenario, given by the maximal steered coherence (MSC). We also obtain a compact expression of the MSC for general X states.

In this paper, we would like to obtain the effect of the quantum backreaction on inflationary Starobinsky cosmology in spatially flat $D$-dimensional Friedmann–Robertson–Walker universe. For this purpose, first, we obtain the vacuum expectation value of energy–momentum tensor, which is separated into two parts, UV and IR. To calculate the UV contribution, we use the WKB approximation of the mode function of the equation of motion. Since the obtained value of this contribution of the vacuum expectation value of energy–momentum tensor is divergent, we should renormalize it. Therefore, by using the dimensional regularization and introducing a counterterm action, we eliminate divergences. After that, we calculate the contributions of IR part and trace anomaly. Thus, we obtain the quantum energy density and pressure during inflation era in this model. Finally, we can find the effect of backreaction on scale factor in inflation era, which leads to the new scale factor.

In this paper, we obtain the effect of backreaction on the scale factor of the Friedmann–Lemaître–Robertson–Walker (FLRW) and de Sitter spaces. We consider a non-minimally coupled massive scalar field to the curvature scalar. For our purpose, we use the results of vacuum expectation values of energy–momentum tensor, which have been obtained previously. By substituting the quantum energy density into the Friedmann equation, we obtain the linear order perturbation of the scale factor. So, the effect of backreaction leads to the new scale factor.

The Elko field of Ahluwalia and Grumiller is a quantum field for massive spin-1/2 particles. It has been suggested as a candidate for dark matter. We discuss our attempts to interpret the Elko field as a quantum field in the sense of Weinberg. Our work suggests that one should investigate quantum fields based on representations of the full Poincaré group which belong to one of the non-standard Wigner classes.