Acceleration and rotation in quantum statistical theory

We study the quark-mass dependence of the QCD critical point at varying bare up/down quark masses with fixed strange quark mass. We explore the corresponding second-order critical surface in the three-dimensional Columbia plot and study the extension of the associated crossover hyperplane at real and imaginary baryon chemical potential. To this end, we employ a by now well-tested combination of lattice Yang–Mills theory and a (truncated) version of Dyson–Schwinger equations at $$N_{f}=2+1$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>N</mml:mi> <mml:mi>f</mml:mi> </mml:msub> <mml:mo>=</mml:mo> <mml:mn>2</mml:mn> <mml:mo>+</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:math> quark flavours. We find evidence for a positive curvature of the second-order surface at (large) real chemical potential and a crossover region for imaginary chemical potential. Our results support the notion of a tricritical point at finite chemical potential in the chiral limit.

Some consequences of the analyticity of the free energy (pressure) of QCD at finite chemical potential are deduced. Lattice simulations at imaginary chemical potential are possible due to the positivity of the measure. We show that such a theory cannot be interpreted as a thermodynamic system with a phase diagram in the usual sense. However, simulations at imaginary chemical potential are useful because the free energy can be analytically continued and information on the thermodynamic system at real chemical potential can be extracted by two means—either by the usual method of Taylor expansions, or by using this data to extract Yang–Lee zeroes of the grand-canonical partition function. We also comment on the structure of zeroes expected for the usual picture of the phases of QCD, following a discussion of the physics of imaginary chemical potential.

Many-body systems with chiral fermions exhibit anomalous transport phenomena originated from quantum anomalies. Based on quantum field theory, we derive the kinetic theory for chiral fermions interacting with an external electromagnetic field and a background curved geometry. The resultant framework respects the covariance under the U(1) gauge, local Lorentz, and diffeomorphic transformations. It is particularly useful to study the gravitational or non-inertial effects for chiral systems. As the first application, we study the chiral dynamics in a rotating coordinate and clarify the roles of the Coriolis force and spin-vorticity coupling in generating the chiral vortical effect (CVE). We also show that the CVE is an intrinsic phenomenon of a rotating chiral fluid, and thus independent of observer's frame.

Despite quantum theory’s remarkable success at predicting the statistical results of experiments, many philosophers worry that it nonetheless lacks some crucial connection between theory and experiment. Such worries constitute the Quantum Measurement Problems. One can broadly identify two kinds of worries: (1) pragmatic: it is unclear how to model our measurement processes in order to extract experimental predictions, and (2) realist: we lack a satisfying metaphysical account of measurement processes. While both issues deserve attention, the pragmatic worries have worse consequences if left unanswered: If our pragmatic theory-to-experiment linkage is unsatisfactory, then quantum theory is at risk of losing both its evidential support and its physical salience. Avoiding these risks is at the core of what I will call the Pragmatic Measurement Problem. Fortunately, the pragmatic measurement problem is not too difficult to solve. For non-relativistic quantum theory, the story goes roughly as follows: One can model each of quantum theory’s key experimental successes on a case-by-case basis by using a measurement chain. In modeling this measurement chain, it is pragmatically necessary to switch from using a quantum model to a classical model at some point. That is, it is pragmatically necessary to invoke a Heisenberg cut at some point along the measurement chain. Past this case-by-case measurement framework, one can then strive for a wide-scoping measurement theory capable of modeling all (or nearly all) possible measurement processes. For non-relativistic quantum theory, this leads us to our usual projective measurement theory. As a bonus, proceeding this way also gives us an empirically meaningful characterization of the theory’s observables as (positive) self-adjoint operators. But how does this story have to change when we move into the context of quantum field theory (QFT)? It is well known that in QFT almost all localized projective measurements violate causality, allowing for faster-than-light signaling; These are Sorkin’s impossible measurements. Thus, the story of measurement in QFT cannot end as it did before with a projective measurement theory. But does this then mean that we need to radically rethink the way we model measurement processes in QFT? Are our current experimental practices somehow misguided? Fortunately not. I will argue that (once properly understood) our old approach to modeling quantum measurements is still applicable in QFT contexts. We ought to first use measurement chains to build up a case-by-case measurement framework for QFT. Modeling these measurement chains will require us to invoke what I will call a QFT-cut. That is, at some point along the measurement chain we must switch from using a QFT model to a non-QFT model. Past this case-by-case measurement framework, we can then strive for both a new wide-scoping measurement theory for QFT and an empirically meaningful characterization of its observables. It is at this point that significantly more theoretical work is needed. This paper ends by briefly reviewing the state of the art in the physics literature regarding the modeling of measurement processes involving quantum fields.

An imaginary-time method was developed for calculating the probability of particle transmission through smooth barriers variable with time. Within the imaginary-time method, the tunneling process is described by using classical equations of motion written in terms of an imaginary time (t → it), while the probability of tunneling is determined by the imaginary part of the action functional, this imaginary part being calculated along the subbarrier particle trajectory. The fundamentals of the imaginary-time method are surveyed, and its applications in the theory of atomic-state ionization under the effect of constant electric and magnetic fields that have various configurations, in the field of intense monochromatic laser radiation and of an ultrashort electromagnetic pulse, in the process of Lorentz ionization of atoms and ions during their motion in a strong magnetic field, etc., are outlined. The applications of the imaginary-time method in relativistic cases—for example, in the theory of ionization of levels of multiply charged ions whose binding energy is commensurate with the electron rest energy—and in quantum field theory (Schwinger effect, which consists in the production of electron-positron pairs from a vacuum by a superstrong external field) are briefly described. Particular attention is given to methodological issues and details of the imaginary-time method that are of importance in solving specific physics problems, but which are usually skipped in original publications.

In this paper we explore the possibility of giving a justification of the “semantic information” content and measure, in the framework of the recent coalgebraic approach to quantum systems and quantum computation, extended to QFT systems. In QFT, indeed, any quantum system has to be considered as an “open” system, because it is always interacting with the background fluctuations of the quantum vacuum. Namely, the Hamiltonian in QFT always includes the quantum system and its inseparable thermal bath, formally “entangled” like an algebra with its coalgebra, according to the principle of the “doubling” of the degrees of freedom (DDF) between them. This is the core of the representation theory of cognitive neuroscience based on QFT. Moreover, in QFT, the probabilities of the quantum states follow a Wigner distribution, based on the notion and measure of quasiprobability, where regions integrated under given expectation values do not represent mutually exclusive states. This means that a computing agent, either natural or artificial, in QFT, against the quantum Turing machine paradigm, is able to change dynamically the representation space of its computations. This depends on the possibility of interpreting QFT system computations within the framework of category theory logic and its principle of duality between opposed categories, such as the algebra and coalgebra categories of QFT. This allows us to justify and not only to suppose, like in the “theory of strong semantic information” of L. Floridi, the definition of modal “local truth” and the notion of semantic information as a measure of it, despite both measures being defined on quasiprobability distributions.

Self-consistent hartree description of finite nuclei in a relativistic quantum field theory

A cat state localized in the right Rindler wedge is employed to study the violation of the Bell-Clauser-Horne-Shimony-Holt (Bell-CHSH) inequality in a relativistic scalar-free quantum field theory. By means of the bounded Hermitian operator <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mrow> <a:mi>sign</a:mi> <a:mo stretchy="false">(</a:mo> <a:mi>φ</a:mi> <a:mo stretchy="false">(</a:mo> <a:mi>f</a:mi> <a:mo stretchy="false">)</a:mo> <a:mo stretchy="false">)</a:mo> </a:mrow> </a:math> , where <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"> <g:mi>φ</g:mi> <g:mo stretchy="false">(</g:mo> <g:mi>f</g:mi> <g:mo stretchy="false">)</g:mo> </g:math> stands for the smeared scalar field, it turns out that the Bell-CHSH correlator can be evaluated in closed analytic form in terms of the imaginary error function. Being the superposition of two coherent states, cat states allow for the existence of interference terms, which give rise to a violation of the Bell-CHSH inequality. As such, the present setup can be considered as an explicit realization of the results obtained by Summers-Werner.

The boundary thermodynamic Bethe Ansatz (BTBA) equations introduced in arXiv:1203.1913 and arXiv:1203.1617 to describe the cusp anomalous dimension contain imaginary chemical potentials and singular boundary fugacities, which make its systematic expansion problematic. We propose an alternative formulation based on real chemical potentials and additional source terms. We expand our equations to double wrapping order and find complete agreement with the direct two-loop gauge theory computation of the cusp anomalous dimension.

We present unambiguous evidence, from lattice simulations of QCD with three degenerate quark species, for two tricritical points in the (T, m) phase diagram at fixed imaginary chemical potential μ/T = iπ/3 mod2π/3, one in the light and one in the heavy mass regime. These represent the boundaries of the chiral and deconfinement critical lines continued to imaginary μ, respectively. It is demonstrated that the shape of the deconfinement critical line for real chemical potentials is dictated by tricritical scaling and implies the weakening of the deconfinement transition with real chemical potential. The generalization to nondegenerate and light quark masses is discussed.

The goal of the present note is to understand whether it is possible to define interacting quantum field theory in global anti de Sitter space-time with Lorentzian signature, in its covering space-time (whose time coordinate is not periodic) and in its Poincare patch. We show that in global anti de Sitter space-time there are certain problems to define quantum field theory properly. This is due to an additional UV singularity of the Feynman propagator which is sitting on the light-cone emanating from the antipodal point of the source. There is no such singularity in flat space-time. At the same time quantum field theory in Poincare region of the AdS space-time can be well defined and is related to the one in Euclidean AdS via the analytical continuation. In principle one can also define and analytically continue quantum field theory in the covering anti de Sitter space-time. However, to do that one has to use an unusual $i\epsilon$-prescription in the Feynman propagator, which cannot be used in loop calculations in non-stationary situations.

The theory of fundamental particles and their non-gravitational interactions is encapsulated by an extremely successful quantum field theory known as the Standard Model. This quantum field theory is determined by a particular set of quantum fields and a particular Hamiltonian, which we will outline in this chapter. It is an interacting quantum field theory, not solvable by the methods we have seen so far. In the non-interacting approximation, it includes just the sorts of free quantum field theories that we have studied in earlier chapters. This chapter gives only a very brief sketch of the definition of the theory; for details, one needs to consult a conventional particle physics textbook.

Of the three organizers of the conference N. Hitchin is a mathematician, A. Kapustin and W. Nahm are physicists. Ideas from physics, in particular from string theory and related areas had a profound influence on algebraic and differential geometry. Conversely, many developments in string theory use very recent mathematical results. There were 19 talks at the workshop, 12 by mathematicians and 7 by physicists, but in many cases an outside observer would have had difficulties to sort them out. Quantum field theory often allows continuous interpolations between geometrical structures of topologically different manifolds. A particularly important example is mirror symmetry, where the complexified Kähler cone of one manifold corresponds to the moduli space of complex structures of the mirror manifold. Several talks explored geometrical and number theoretical aspects of this connection. Mirror symmetry can be understood in terms of torus fibrations and an isomorphism between the quantum field theories given by maps to a torus and to its dual (T-duality). The B-field of string theory can be described in terms of non-commutative geometry on the tori, and its effect on T-duality has been investigated. The quantum field theories which provide these dualities are supersymmetric conformally invariant quantum field theories in two dimensions. In mathematics, large parts of their structures have been axiomatised in the language of vertex operator algebras, but much remains to be done. A promising mathematical approach is provided by the chiral de Rham complex. This cohomology of this complex seems to be invariant under mirror symmetry, but its physical meaning is not yet clear. This led to many discussions between mathematicians and physicists. Indeed, the free time for discussions was at least as important as the lectures for learning the language of researchers with a different background and for making use of their ideas. An area in which the common understanding is well advance is topological field theory. Here one has good axioms and many of the analytic problems of conformally invariant quantum field theories can be ignored. One can solve rather complex problems and one can make contact with new geometrical ideas, in particular generalised complex structures. The latter allow to interpolate between complex and symplectic geometry, which should become important for both physics and mathematics. To understand all of conformal field theory at a similar mathematical depth will take more time, but already now relations to mixed Hodge structures have given much insight. Eventually many so far intractable problems should be solvable by the use of quantum field theoretical ideas, for example the construction of the non-singular Ricci flat metrics on K3. Perturbative string theory can be described in terms of conformal field theory, but the complete theory has more excitations than strings. Among them the best understood are the D-branes, many features of which can be understood in terms of boundary states in conformal field theory. Some of these branes are related to complex submanifolds, others to certain Lagrangian submanifolds, and their description involves twisted K-theory and derived categories. The development of a common language between mathematicians and physicists is well under way, and the workshop has made a contribution which all participants found very stimulating. In Europe such meetings between mathematicians and string theorists are rare, so the workshop was particularly useful. Much of the time was reserved for informal discussions. On one evening there was a discussion on the relation between classical and quantum geometry. Weather predictions for the free afternoon had been bad, but finally the weather was splendid and the supply of Black Forest cake matched the demand.

We briefly exhibit in this chapter the mathematical formalism of QFT, which actually has a non-trivial combinatorial backbone. The QFT setting can be understood as a quantum description of particles and their interactions, a description which is also compatible with Einstein's theory of special relativity. Within the framework of elementary particle physics (or high-energy physics), QFT led to the Standard Model of Elementary Particle Physics, which is the physical theory tested with the best accuracy by collider experiments. Moreover, the QFT formalism successfully applies to statistical physics, condensed matter physics and so on. We show in this chapter how Feynman graphs appear through the so-called QFT perturbative expansion, how Feynman integrals are associated to Feynman graphs and how these integrals can be expressed via the help of graph polynomials, the Kirchhoff–Symanzik polynomials. Finally, we give a glimpse of renormalization, of the Dyson–Schwinger equation and of the use of the so-called intermediate field method. This chapter mainly focuses on the so-called Phi? QFT scalar model.

The quantum field theory (QFT) is one of branches of the Standard Model. According to QFT, quantum fields are the primary entities and particles are the excitations of these fields, coming in discrete lumps with no inner structures and with properties assigned by declaration. Such view is in conflict with the observed vacuum energy density, 140 orders of magnitudes less than required by the QFT. In addition, such view is challenged by Aphysical Quantum Mechanics (AQM), a deeper quantum theory. According to AQM, the fundamental understanding of quantum reality is expanded by the addition of two fundamental categories, aphysical and elementary consciousness of elementary particles. Based on AQM and as an example, the total ontology of the intrinsic (fundamental) electron is presented with its inner structure of perfect geometry consisting of the physical charged c-ring and aphysical cylinder, and with its properties such as self-mass, spin, magneto-electrostatic field configuration and magnetic moment. The position parameter in the inner structure demonstrates that there are no two identical intrinsic electrons in the Universe thus placing a question mark over the QFT principle of indistinguishability.