The Pivotal Role of Causality in Local Quantum Physics

In this article an attempt is made to present very recent conceptual and computational developments in QFT as new manifestations of old and well establihed physical principles. The vehicle for converting the quantum-algebraic aspects of local quantum physics into more classical geometric structures is the modular theory of Tomita. As the above named laureate to whom I have dedicated has shown together with his collaborator for the first time in sufficient generality, its use in physics goes through Einstein causality. This line of research recently gained momentum when it was realized that it is not only of structural and conceptual innovative power (see section 4), but also promises to be a new computational road into nonperturbative QFT (section 5) which, picturesquely speaking, enters the subject on the extreme opposite (noncommutative) side.Comment: This is a updated version which has been submitted to Journal of Physics A, tcilatex 62 pages. Adress: Institut fuer Theoretische Physik FU-Berlin, Arnimallee 14, 14195 Berlin presently CBPF, Rua Dr. Xavier Sigaud 150, 22290-180 Rio de Janeiro, Brazi

New Concepts in Particle Physics from Solution of an Old Problem

Recent ideas on modular localization in local quantum physics are used to clarify the relation between on- and off-shell quantities in particle physics; in particular the relation between on-shell crossing symmetry and off-shell Einstein causality. Among the collateral results of this new nonperturbative approach are profound relations between crossing symmetry of particle physics and Hawking-Unruh like thermal aspects (KMS property, entropy attached to horizons) of quantum matter behind causal horizons, aspects which hitherto were exclusively related with Killing horizons in curved spacetime rather than with localization aspects in Minkowski space particle physics. The scope of this modular framework is amazingly wide and ranges from providing a conceptual basis for the d=1+1 bootstrap-formfactor program for factorizable d=1+1 models to a decomposition theory of QFT's in terms of a finite collection of unitarily equivalent chiral conformal theories placed a specified relative position within a common Hilbert space (in d=1+1 a holographic relation and in higher dimensions more like a scanning). The new framework gives a spacetime interpretation to the Zamolodchikov-Faddeev algebra and explains its thermal aspects.Comment: In this form it will appear in JPA Math Gen, 47 pages tcilate

Massive Vector Mesons and Gauge Theory

We show that the requirements of renormalizability and physical consistency imposed on perturbative interactions of massive vector mesons fix the theory essentially uniquely. In particular physical consistency demands the presence of at least one additional physical degree of freedom which was not part of the originally required physical particle content. In its simplest realization (probably the only one) these are scalar fields as envisaged by Higgs but in the present formulation without the ``symmetry-breaking Higgs condensate''. The final result agrees precisely with the usual quantization of a classical gauge theory by means of the Higgs mechanism. Our method proves an old conjecture of Cornwall, Levin and Tiktopoulos stating that the renormalization and consistency requirements of spin=1 particles lead to the gauge theory structure (i.e. a kind of inverse of 't Hooft's famous renormalizability proof in quantized gauge theories) which was based on the on-shell unitarity of the $S$-matrix. We also speculate on a possible future ghostfree formulation which avoids ''field coordinates'' altogether and is expected to reconcile the on-shell S-matrix point of view with the off-shell field theory structure.Comment: 53 pages, version to appear in J. Phys.

Upgrade of the BOC for the ATLAS Pixel Insertable B-Layer

The phase 1 upgrade of the ATLAS [1] pixel detector will be done by inserting a fourth pixel layer together with a new beampipe into the recent three layer detector. This new detector, the Insertable B-Layer (IBL) should be integrated into the recent pixel system with as few changes in services as possible, but deliver some advantages over the recent system. One of those advantages will be a new data transmission link from the detector modules to the off-detector electronics, requiring a re-design of the electro-optical converters on the off-detector side. First ideas of how to implement those, together with some ideas to reduce cost by increasing the systems throughput are discussed

Elliptic Thermal Correlation Functions and Modular Forms in a Globally Conformal Invariant QFT

Global conformal invariance (GCI) of quantum field theory (QFT) in two and higher space-time dimensions implies the Huygens' principle, and hence, rationality of correlation functions of observable fields (see Commun. Math. Phys. 218 (2001) 417-436; hep-th/0009004). The conformal Hamiltonian $H$ has discrete spectrum assumed here to be finitely degenerate. We then prove that thermal expectation values of field products on compactified Minkowski space can be represented as finite linear combinations of basic (doubly periodic) elliptic functions in the conformal time variables (of periods 1 and $\tau$) whose coefficients are, in general, formal power series in $q^{1/2}=e^{i\pi\tau}$ involving spherical functions of the "space-like" fields' arguments. As a corollary, if the resulting expansions converge to meromorphic functions, then the finite temperature correlation functions are elliptic. Thermal 2-point functions of free fields are computed and shown to display these features. We also study modular transformation properties of Gibbs energy mean values with respect to the (complex) inverse temperature $\tau$ ($Im(\tau)=\beta/(2\pi)>0$). The results are used to obtain the thermodynamic limit of thermal energy densities and correlation functions.Comment: LaTex. 56 pages. The concept of global conformal invariance set in a historical perspective (new Sect. 1.1 in the Introduction), references added; minor corrections in the rest of the pape

Axiomatic formulations of nonlocal and noncommutative field theories

We analyze functional analytic aspects of axiomatic formulations of nonlocal and noncommutative quantum field theories. In particular, we completely clarify the relation between the asymptotic commutativity condition, which ensures the CPT symmetry and the standard spin-statistics relation for nonlocal fields, and the regularity properties of the retarded Green's functions in momentum space that are required for constructing a scattering theory and deriving reduction formulas. This result is based on a relevant Paley-Wiener-Schwartz-type theorem for analytic functionals. We also discuss the possibility of using analytic test functions to extend the Wightman axioms to noncommutative field theory, where the causal structure with the light cone is replaced by that with the light wedge. We explain some essential peculiarities of deriving the CPT and spin-statistics theorems in this enlarged framework.Comment: LaTeX, 13 pages, no figure

Four Dimensional CFT Models with Rational Correlation Functions

Recently established rationality of correlation functions in a globally conformal invariant quantum field theory satisfying Wightman axioms is used to construct a family of soluble models in 4-dimensional Minkowski space-time. We consider in detail a model of a neutral scalar field $\phi$ of dimension 2. It depends on a positive real parameter c, an analogue of the Virasoro central charge, and admits for all (finite) c an infinite number of conserved symmetric tensor currents. The operator product algebra of $\phi$ is shown to coincide with a simpler one, generated by a bilocal scalar field $V(x_1,x_2)$ of dimension (1,1). The modes of V together with the unit operator span an infinite dimensional Lie algebra $L_V$ whose vacuum (i.e. zero energy lowest weight) representations only depend on the central charge c. Wightman positivity (i.e. unitarity of the representations of $L_V$) is proven to be equivalent to $c \in N$.Comment: 28 pages, LATEX, amsfonts, latexsym. Proposition 2.3, and Conjecture in Sec. 6 are revised. Minor errors are correcte

Applications of Canonical Transformations

Canonical transformations are defined and discussed along with the exponential, the coherent and the ultracoherent vectors. It is shown that the single-mode and the $n$-mode squeezing operators are elements of the group of canonical transformations. An application of canonical transformations is made, in the context of open quantum systems, by studying the effect of squeezing of the bath on the decoherence properties of the system. Two cases are analyzed. In the first case the bath consists of a massless bosonic field with the bath reference states being the squeezed vacuum states and squeezed thermal states while in the second case a system consisting of a harmonic oscillator interacting with a bath of harmonic oscillators is analyzed with the bath being initially in a squeezed thermal state.Comment: 14 page

Is the brick-wall model unstable for a rotating background?

The stability of the brick wall model is analyzed in a rotating background. It is shown that in the Kerr background without horizon but with an inner boundary a scalar field has complex-frequency modes and that, however, the imaginary part of the complex frequency can be small enough compared with the Hawking temperature if the inner boundary is sufficiently close to the horizon, say at a proper altitude of Planck scale. Hence, the time scale of the instability due to the complex frequencies is much longer than the relaxation time scale of the thermal state with the Hawking temperature. Since ambient fields should settle in the thermal state in the latter time scale, the instability is not so catastrophic. Thus, the brick wall model is well defined even in a rotating background if the inner boundary is sufficiently close to the horizon.Comment: Latex, 17 pages, 1 figure, accepted for publication in Phys. Rev.

Charge-dependent interactions of monomeric and filamentous actin with lipid bilayers

The cytoskeletal protein actin polymerizes into filaments that are essential for the mechanical stability of mammalian cells. In vitro experiments showed that direct interactions between actin filaments and lipid bilayers are possible and that the net charge of the bilayer as well as the presence of divalent ions in the buffer play an important role. In vivo, colocalization of actin filaments and divalent ions are suppressed, and cells rely on linker proteins to connect the plasma membrane to the actin network. Little is known, however, about why this is the case and what microscopic interactions are important. A deeper understanding is highly beneficial, first, to obtain understanding in the biological design of cells and, second, as a possible basis for the building of artificial cortices for the stabilization of synthetic cells. Here, we report the results of coarse-grained molecular dynamics simulations of monomeric and filamentous actin in the vicinity of differently charged lipid bilayers. We observe that charges on the lipid head groups strongly determine the ability of actin to adsorb to the bilayer. The inclusion of divalent ions leads to a reversal of the binding affinity. Our in silico results are validated experimentally by reconstitution assays with actin on lipid bilayer membranes and provide a molecular-level understanding of the actin-membrane interaction.</p