Giuliano Preparata

Operator product expansions near the light cone

Abstract The behaviour of products A(x)B(0) of local field operators near the light cone x2 = 0 is studied in renormalized perturbation theory. Operator product expansions are shown to exist and describe this behaviour in each order. This result is an extensive generalization of known results about short distance (xμ → 0) behaviour in quantum field theory. For example, the local scalar current j(x) ≡ : ϕ(x)ϕ(x) : of dimension two in ϕ4 theory, ignoring logs and c-numbers, has the short distance behaviour j(x)j(0) → x→0 c 0 1 x 2 j(0)+c 1 1 x 2 xα:φ∂αφ. It is shown that the light cone behaviour is j(x)j(0) → x 2 →0 1 x 2 ∑ n=0 ∞ x αn …x αn 0 (n) α 1 …α n (0) for some necessarily infinite set 0 (n) α1…αn of local field operators satisfying dim O(n)α1…αn = n+ 2. One must have O(o) = c0j and O(1)α1 = c1 : ϕ∂α1ϕ:, and the ifO(n) for n ⩾ 2 do not contribute for xμ → 0 but they are necessary to describe the x2 → 0 limit. Similar expansions are derived for the product jμ(x)jν(0) of vector currents and for other interesting products in ϕ4 theory, the gluon model, all other renormalizable models, and in soluble field theoretic models. Properties of the expansions are discussed in detail. The usefulness of such expansions arises from the fact that they describe, for example, the configuration space limit corresponding to the physical momentum space limit in which a very massive current interacts with a hadronic system in a high energy inelastic collision. The operator expansions predict the strength of the light cone singularities and thereby provide a means of measuring the dimensions of inteacting fields, they determine properties of amplitudes in several variables, and they provide relations between form factors describing different experiments corresponding to different matrix elements of the current products. Several such applications are described and it is concluded that the present experimental results are in good agreement with the naive field dimensions and canonical singularity structure of renormalizable field theories.

QED coherence and the thermodynamics of water

It is shown that when the density becomes larger than a critical density an ensemble of water molecules evolves towards a coherent ground state, where molecules oscillate in phase with the e.m. field. At each temperature, liquid water is found to consist of a coherent phase of molecules in such a ground state and of a normal phase, whose population is determined by thermal excitations. The observed thermodynamical quantities as well as their wellknown anomalous behaviors are satisfactorily described by our theory.

Coherent Electrodynamics in Water

The phenomenological properties of water are shown to be inconsistent with the generally accepted approach to condensed matter, whose basic assumption is that interactions between molecules are electrostatic and short range. On the contrary, Quantum Electrodynamics (QED) is seen to play a key role in the existence of the liquid state. In particular, a collective dynamics emerges, which could have significant biological implications.

ELECTRODYNAMICAL COHERENCE IN WATER: A POSSIBLE ORIGIN OF THE TETRAHEDRAL COORDINATION

In the conceptual framework of Coherent Quantum Electrodynamics we show that the molecules of the liquid phase are described by individual quantum states that differ from those in which the molecules find themselves while in the gas phase. We suggest that tetrahedral coordination emerges from such individual configurations.

Possible Theories of Cold Fusion.

SummaryWe review some of the key facts in the phenomenology of Pd-hydrides usually referred to as «cold fusion». We conclude that all theoretical attempts that concentrate only on few-body interactions, both electromagnetic and nuclear, are probably insufficient to explain such phenomena. On the other hand we find good indications that theories describing collective, coherent interactions among elementary constituents leading tomacroscopic quantum-mechanical effects belong to the class of possible theories of those phenomena.

Anisotropic yang-mills interactions for quarks and leptons

SummaryA new (seven-dimensional) geometrical structure is proposed for the physical event continuum that allows us to formulate gauge (anisotropic Yang-Mills) interactions for quarks and leptons. A Dyson analysis of the resulting quantum field theory shows a bifurcation between chiral and nonchiral interactions, the former giving rise to unconfined leptons and the standardSU2,L ×U1 description of electroweak interactions, the latter leading to confined quarks. For the electroweak theory we calculate (to lowest order in the original coupling constants) sin2ϑW=1/4. A brief discussion of the structure of the hadronic world emerging from theSU3,colour interaction is presented.RiassuntoSi propone una nuova struttura geometrica a sette dimensioni per il continuo degli eventi fisici, in modo da permettere la formulazione di un’interazione di gauge tra quark e leptoni (interazioni di Yang-Mills anisotrope). Un’analisi delle equazioni di Dyson della conseguente teoria di campo quantistica mostra una biforcazione fra teorie chirali e non chirali, le prime producono leptoni non confinati mentre le seconde danno luogo a quark confinati. Inoltre nel caso della teoria elettrodebole si ottiene (all’ordine piú basso) sin2ϑW=1/4. Si presenta infine una discussione del mondo adronico emergente dall’interazioneSU3, colore.РеэюмеПредлагается новая (семимерная) геометрическая структура для фиэического континуума событий, что поэволяет сформулировать калибровочные вэаимодействия (аниэотропные вэаимодействия Янга-Миллса) для кварков и лептонов. Аналиэ Дайсона полученной квантовой теории поля обнаруживает раэдвоение между киральными и некиральными вэаимодействиями. Киральные вэаимодействия при-водят к неограниченным лептонам и стандартномуSU2,L ×U1 описанию злектрослабых вэаимодействий. Некиральные вэаимодействия приводят к ограниченным кваркам. Для злектрослабой теории мы вычисляем (в ниэщем порядке по исходной константе свяэи) sin2 ϑW=1/4. Предлагается обсуждение структуры адронного мира, который воэникает иэSU3, colour-вэаимодействия.

Anisotropic Chromodynamics and the QCD Ground State.

SummaryAnisotropic chromodynamics (ACD), a color gauge theory on a postulated anisotropic space-time proposed long ago, is seen to emerge as the effective theory of quarks and gluons on what most likely is the QCD ground state, the chromo magnetic liquid (CML). A description of both the kinematics and dynamics of ACD is presented, and a possible strategy for a systematic calculation of hadronic physics is outlined.

DICKE HAMILTONIAN AND SUPERRADIANT PHASE TRANSITIONS

We show that a correct analysis of the gauge-invariance properties of the em coupling of atomic systems with single-mode em radiation fields allows to overcome the “no-go” theorem for superradiant phase transitions in systems governed by the Dicke Hamiltonian

The standard model on a Planck lattice: Mixing angles versus quark masses

SummaryProceeding in our research programme on the Standard Model (SM) on a Planck lattice (PLSM) we analyse the emergence of the quark masses through a «superconducting» mechanism of spontaneous violation of the chiral symmetry of the Standard Model. Due to the peculiar structure of the lattice coupling of the W± gauge bosons, we discover four new relationships between the angles of the mixing matrix and the (current) quark masses. In particular, we predict theCP-violating phase δ13 °.