Particles, Volume 2, Issue 1 (March 2019) – 11 articles

The problem of pressure fluctuations in the thermal equilibrium state of some objects is discussed, its solution being suggested via generalizing the Bogoliubov–Zubarev theorem. This theorem relates the thermodynamic pressure with the Hamilton function and its derivatives describing the object in question. It is shown that unlike to other thermodynamic quantities (e.g., the energy or the volume) the pressure fluctuations are described not only by a purely thermodynamic quantity (namely, the corresponding thermodynamic susceptibility) but also by some non-thermodynamic quantities. The attempt is made to apply these results to the relativistic ideal gases, with some numerical results being valid for the limiting ultra-relativistic or high-temperature case. Full article

We study the particle production in the early stage of the ultrarelativistic heavy-ion collisions. To this end the Boltzmann kinetic equations for gluons and pions with elastic rescattering are considered together with a simple model for the parton-hadron conversion process (hadronisation). It is shown that the overpopulation of the gluon phase space in the initial state leads to an intermediate stage of Bose enhancement in the low-momentum gluon sector which due to the gluon-pion conversion process is then reflected in the final distribution function of pions. This pattern is very similar to the experimental finding of a low-momentum pion enhancement in the ALICE experiment at the CERN Large Hadron Collider (LHC). Relations to the thermal statistical model of hadron production and the phenomenon of thermal and chemical freeze-out are discussed in this context. Full article

Nonlocal quantum theory of a one-component scalar field in D-dimensional Euclidean spacetime is studied in representations of $\mathcal{S}$ -matrix theory for both polynomial and nonpolynomial interaction Lagrangians. The theory is formulated on coupling constant g in the form of an infrared smooth function of argument x for space without boundary. Nonlocality is given by the evolution of a Gaussian propagator for the local free theory with ultraviolet form factors depending on ultraviolet length parameter l. By representation of the $\mathcal{S}$ -matrix in terms of abstract functional integral over a primary scalar field, the $\mathcal{S}$ form of a grand canonical partition function is found. By expression of $\mathcal{S}$ -matrix in terms of the partition function, representation for $\mathcal{S}$ in terms of basis functions is obtained. Derivations are given for a discrete case where basis functions are Hermite functions, and for a continuous case where basis functions are trigonometric functions. The obtained expressions for the $\mathcal{S}$ -matrix are investigated within the framework of variational principle based on Jensen inequality. Through the latter, the majorant of $\mathcal{S}$ (more precisely, of $-ln\mathcal{S}$ ) is constructed. Equations with separable kernels satisfied by variational function q are found and solved, yielding results for both polynomial theory ${\phi }^4$ (with suggestions for ${\phi }^6$ ) and nonpolynomial sine-Gordon theory. A new definition of the $\mathcal{S}$ -matrix is proposed to solve additional divergences which arise in application of Jensen inequality for the continuous case. Analytical results are obtained and numerically illustrated, with plots of variational functions q and corresponding majorants for the $\mathcal{S}$ -matrices of the theory. For simplicity of numerical calculation, the $D=1$ case is considered, and propagator for free theory G is in the form of Gaussian function typically in the Virton–Quark model, although the obtained analytical inferences are not, in principle, limited to these particular choices. Formulation for nonlocal QFT in momentum k space of extra dimensions with subsequent compactification into physical spacetime is discussed, alongside the compactification process. Full article

Our aim is to contribute to quantum field theory (QFT) formalisms useful for descriptions of short time phenomena, dominant especially in heavy ion collisions. We formulate out-of-equilibrium QFT within the finite-time-path formalism (FTP) and renormalization theory (RT). The potential conflict of FTP and RT is investigated in $g{\varphi }^3$ QFT, by using the retarded/advanced ( $R/A$ ) basis of Green functions and dimensional renormalization (DR). For example, vertices immediately after (in time) divergent self-energy loops do not conserve energy, as integrals diverge. We “repair” them, while keeping $d<4$ , to obtain energy conservation at those vertices. Already in the S-matrix theory, the renormalized, finite part of Feynman self-energy ${\Sigma }_F(p_0)$ does not vanish when $|p_0|\to \infty$ and cannot be split to retarded and advanced parts. In the Glaser–Epstein approach, the causality is repaired in the composite object $G_F(p_0){\Sigma }_F(p_0)$ . In the FTP approach, after repairing the vertices, the corresponding composite objects are $G_R(p_0){\Sigma }_R(p_0)$ and ${\Sigma }_A(p_0)G_A(p_0)$ . In the limit $d\to 4$ , one obtains causal QFT. The tadpole contribution splits into diverging and finite parts. The diverging, constant component is eliminated by the renormalization condition $⟨0\left|\varphi \right|0⟩=0$ of the S-matrix theory. The finite, oscillating energy-nonconserving tadpole contributions vanish in the limit $t\to \infty$ . Full article

We review our recent works on polarization-sensitive electro-optic (PS-EO) sampling, which is a method that allows us to measure elliptically-polarized terahertz time-domain waveforms without using wire-grid polarizers. Because of the phase mismatch between the employed probe pulse and the elliptically-polarized terahertz pulse that is to be analyzed, the probe pulse senses different terahertz electric-field (E-field) vectors during the propagation inside the EO crystal. To interpret the complex condition inside the EO crystal, we expressed the expected EO signal by “frequency-domain description” instead of relying on the conventional Pockels effect description. Using this approach, we derived two important conclusions: (i) the polarization state of each frequency component can be accurately measured, irrespective of the choice of the EO crystal because the relative amplitude and phase of the E-field of two mutually orthogonal directions are not affected by the phase mismatch; and, (ii) the time-domain waveform of the elliptically-polarized E-field vector can be retrieved by considering the phase mismatch, absorption, and the effect of the probe pulse width. We experimentally confirm the above two conclusions by using different EO crystals that are used for detection. This clarifies the validity of our theoretical analysis based on the frequency-domain description and the usefulness of PS-EO sampling. Full article

Recent experimental results about the energy behavior of the total cross sections, the share of elastic and inelastic contributions to them, the peculiar shape of the differential cross section and our guesses about the behavior of real and imaginary parts of the elastic scattering amplitude are discussed. The unitarity condition relates elastic and inelastic processes. Therefore it is used in the impact-parameter space to get some information about the shape of the interaction region of colliding protons by exploiting new experimental data. The obtained results are described. Full article

Gravitational waves, electromagnetic radiation, and the emission of high energy particles probe the phase structure of the equation of state of dense matter produced at the crossroad of the closely related relativistic collisions of heavy ions and of binary neutron stars mergers. 3 + 1 dimensional special- and general relativistic hydrodynamic simulation studies reveal a unique window of opportunity to observe phase transitions in compressed baryon matter by laboratory based experiments and by astrophysical multimessenger observations. The astrophysical consequences of a hadron-quark phase transition in the interior of a compact star will be focused within this article. Especially with a future detection of the post-merger gravitational wave emission emanated from a binary neutron star merger event, it would be possible to explore the phase structure of quantum chromodynamics. The astrophysical observables of a hadron-quark phase transition in a single compact star system and binary hybrid star merger scenario will be summarized within this article. The FAIR facility at GSI Helmholtzzentrum allows one to study the universe in the laboratory, and several astrophysical signatures of the quark-gluon plasma have been found in relativistic collisions of heavy ions and will be explored in future experiments. Full article

A magnetic chicane bunch compressor for a new compact accelerator-based terahertz (THz) radiation source at the Institute of Advanced Energy, Kyoto University, was completely installed in March 2016. The chicane is employed to compress an electron bunch with an energy of 4.6 MeV generated by a 1.6-cell photocathode radio frequency (RF)-gun. The compressed bunch is injected into a short planar undulator for THz generation by coherent undulator radiation (CUR). The characteristics of the bunch compressor and the compressed bunch were investigated by observing the coherent transition radiation (CTR). The CTR spectra, which were analyzed by using a Michelson interferometer, and the compressed bunch length were also estimated. The results were that the chicane could compress the electron bunch at a laser injection phase less than 45 degrees, and the maximum CTR intensity was observed at a laser injection phase around 24 degrees. The optimum value of the first momentum compaction factor was around −45 mm, which provided an estimated rms bunch length less than 1 ps. Full article

One of the very first applications of the quantum field theoretic vacuum state was in the development of the notion of Casimir energy. Now, field theoretic Casimir energies, considered individually, are always infinite. However, differences in Casimir energies (at worst regularized, not renormalized) are quite often finite—a fortunate circumstance which luckily made some of the early calculations, (for instance, for parallel plates and hollow spheres), tolerably tractable. We will explore the extent to which this observation can be made systematic. For instance: What are necessary and sufficient conditions for Casimir energy differences to be finite (with regularization but without renormalization)? Additionally, when the Casimir energy differences are not formally finite, can anything useful nevertheless be said by invoking renormalization? We will see that it is the difference in the first few Seeley–DeWitt coefficients that is central to answering these questions. In particular, for any collection of conductors (be they perfect or imperfect) and/or dielectrics, as long as one merely moves them around without changing their shape or volume, then physically the Casimir energy difference (and so also the physically interesting Casimir forces) is guaranteed to be finite without invoking any renormalization. Full article