G. Jacob

Quasi-free scattering with polarized protons

Abstract Asymmetric (p, 2p) reactions induced by polarized protons are analysed. The nuclear absorption and refraction enhances the cross section for the knock-out of protons with a certain polarization direction which depends on their momentum and on the resulting hole state. The expected pronounced and strongly angle dependent asymmetries in the correlation distributions are calculated for the quasi-stationary hole states of 16 O and 40 Ca.

Probing the spin-orbit coupling of nuclear protons

Abstract The strong absorption in quasi-free scattering opens a possibility of measuring the spin-orbit coupling of nuclear protons. Cross sections for polarized incoming protons are expected to exhibit pronounced asymmetries, with size and sign depending on the selected momentum and the spin-orbit coupling in the nuclear state involved.

A remark on nuclear hole states in quasi-free scattering

Abstract Without adding basic complications, an improvement in the usual approximation of the overlap integral occuring in the cross section for quasi-free scattering is achieved by replacing the single-particle state by a hole state bound in a complex potential. The effect of the finite lifetime of hole states on the angular correlation distributions is estimated.

Broken symmetries and the electron-muon problem

SummaryThe fermion propagators in the quantum electrodynamics of the combined fields of electrons and muons with zero bare masses have been investigated. The basic theory possesses various symmetry properties which are not present in the vacuum. This results in a non-uniqueness of the mathematical description, and equivalence classes for the fermion propagators have been defined. In the approximation used it has been shown that a meaningful vacnum correlation of the two lepton fields is incompatible with an exactly parity invariant vacuum.RiassuntoSi sono studiati i propagatori fermionici nell’elettrodinamica quantistica dei campi combinati degli elettroni e dei muoni con masse nude nulle. La teoria fondamentale possiede varie proprietà di simmetria che non sono presenti nel vuoto. Ne risulta una non unicità della descrizione matematica, e si sono quindi definite le classi di equivalenza dei propagatori fermionici. Si è dimostrato, nell’approssimazione usata, che una significativa correlazione del vuoto dei due campi leptonici è incompatibile con un vuoto esattamente invariante rispetto alla parità.

Two ways of spontaneous symmetry breaking

SummaryA distinction between two types of spontaneous sym metry breakings is made: “asymptotical” breaking and “local” breaking. The former is characterized by a conserved symmetry current and by the presence of Goldstone bosons (or long-range interactions), and occurs in the BCS-theory as well as in classical theories. For local breakings the usual proof of current conservation breaks down as a result of the singularity of a product of field operators at one point, as occurring in currents and their divergences. This case is realized in certain local quantum field theories,e.g. in quantum electrodynamics with zero bare mass. Local breakings, in contradistinction to asymptotical ones, might be useful in a field theory of elementary particles.RiassuntoSi distingue fra due tipi di rottura spontanea della simmetria: quella “asintotica” e quella “locale”. La prima è caratterizata da una corrente di simmetria conservata e dalla presenza di bosoni di Goldstone (oppure di interazioni a lungo raggio), e si verifica tanto nella teoria di BCS che in quella classica. Per le rotture locali la consueta prova di conservazione della corrente viene meno come risultato della singolarità del proclotto degli operatori di campo in un punto, come accade nelle correnti e le loro divergenze. Questo caso si verifica in alcune teorie di campo locale quantizzato, per esempio l’elettrodinamica quantistica con massa nuda nulla. Le rotture locali, contrariamente a quelle asintotiche, possono essere utilizzate in una teoria di campo per le particelle elementari.РезюмеДелается различие между двумя типами спонтанного нарушения симметрии: “асимптотическое” нарушение и “локальное” нарушение. Первый тип характеризуется сохраняющимся симметричным током и наличием бозонов Голдстоуна (или дальнодействующими взаимодействиями) и встречается в BCS-теории так же, как и в классических теориях. Для локальных нарушений обычное доказательство сохранения тока нарушается как результат синтулярности произведения операторов поля в одной точке, встречающееся в токах и их производных. Этот случай реализуется в локальных квантовых теориях поля, т.е. в квантовых электродинамиках с нулевой затравочной массой. Локальные нарушения, в отличие от асимптотических нарушений, могут быть использованы в теории поля элементарных частиц.

A GENERALIZATION OF THE LANDAU GAUGE

SummaryA gauge has been derived in which the γp-part of the self-energy integral for the electron, with Гώ = constant · γώ but with arbitrary photon and electron propagators, vanishes identically. For the special case of the free photon propagator this diagonalizing gauge is the Landau gauge. Using this generalized Landau gauge the Dyson equation for the electron propagator, in which only the approximation Г = constant · γώ has been made, reduces to an integral equation for one scalar function.RiassuntoSi è dedotta vina gauge in oui la parte γp dell’integrale dell’autoenergia dell’elettrone, conTώ = const · γώ ma con propagatori fotonici ed elettronici arbitrari, si annulla identicamente. Nel caso speciale del propagatore del fotone libero questa gauge diagonale è la gauge di Landau. Facendo uso di questa gauge di Landau generalizzata l’equazione di Dyson per il propagatore elettronico, in oui si è fatta solo l’approssimazione Гώ = cost · γώ, si riduce ad un’equazione integrale per una funzione scalare.

RENORMALIZATION AND GAUGE INVARIANCE IN QUANTUM ELECTRODYNAMICS.

The connection between the field theory and the perturbation expansion of quantum electrodynamics is studied. As a starting point the usual Lagrangian is taken but with bare electron mass and the renormalization constant Z3 set equal to zero. This theory is essentially equivalent to the usual one; however, it does not contain any constant of nature and is dilatational and gauge invariant, both invariances being spontaneously broken. The various limiting procedures implied by the differentiation, the multiplication and the renormalization of the field operators in the Lagrangian are combined in a gauge invariant way to a single limit. Propagator equations are derived which are the usual renormalized ones, except for: (i) a natural cancellation of the quadratic divergence of the vacuum polarization; (ii) the presence of an effective cutoff at p ≈ ϵ−1; (iii) the replacement of the renormalization constants Z1 and Z2 by one gauge dependent function Z(ϵ2); (iv) the limit ϵ → 0 which has to be taken. The value Z(0) corresponds to the usual constants Z1 and Z2. It is expected that in general Z(0) = 0, but this poses no problem in the present formulation. It is argued that the function Z(ϵ2), which is determined by the equations, may render the vacuum polarization finite. One may eliminate the renormalization function from the propagator equations and then perform the limit ϵ → 0; this results in the usual perturbation series. However, the renormalization function is essential for an understanding of the high momentum behaviour and of the relation between the field theory and the perturbation expansion.

Charge commutator for any momentum

Abstract The nucleon matrix elements of the charge commutation relations are considered for arbitrary momentum. The resulting expression is exact. The high-momentum limit reduces to the Alder-Weisberger sum rule. For zero momentum one obtains the known low-energy result together with a closed expression for the correction.

Degrees of symmetry in quantum field theories

Abstract A hierarchy of possible symmetries in quantum field theory is defined, which reaches from a purely mathematical invariance to the conventional physical invariance, including the commonly discussed type of spontaneously broken symmetry (SBS). It is shown that one type of SBS, which is usually not considered, naturally leads to theories with an algebra of non-conserved currents and a non-linearly transforming phenomenological Lagrangian. An exactly solvable model is given and some general remarks are made.

The length scale in quantum electrodynamics without a bare mass

SummaryA definite length scale in Quantum Electrodynamics without a bare mass can only be induced by a coupling with another system. This problem is studied in a model consisting of one charged « neutrino » field and charged strongly interacting particle fields. A criterion is derived which is similar to the principle of extremalization of the energy in Mechanics. The approximation used allows only the conclusion that the ratio between the lepton mass and the strongly interacting particle masses is not of zeroth order in the renormalized electromagnetic coupling. constant.RiassuntoNell’elettrodinamica quantistica con massa nuda zero, si può indurre uua scala di lunghezze deflnita solo con l’accoppiamento ad un altro sistema. Si studia il problema su un modello costituito da un campo di« neutrini » carico e da campi di particelle cariche fortemente interagenti. Si ricava un criterio simile all’estrazione dell’energia in meccanica. L’approssimazione usata permette solo la conclusione che il rapporte tra la massa del leptone e le masse delle particelle fortemente interagenti non è d’ordine zero nella costante d’accoppiamento elettromagnetico rinormalizzata.