An •interesting and until now unanswered question is how quarks, confined within a bag, interact ... more An •interesting and until now unanswered question is how quarks, confined within a bag, interact when their number is very large. , Can their residual interaction be understood in terms of perturbation theory or is it basically non-perturbative? As remote as any other possibility is to assume the quarks to be free within the bag, when the total baryon number corresponds to that of giant nuclei. We investigate here such giant quark bags with baryon numbers up to 1000. Experimental consequences and some spepulations in connection with the recently observed anomalous positron production are discussed. This report was done with support from the Department of Energy. Any conclusions or opinions expressed in this report represent solely those of the author(s) and not necessarily those of The Regents of the University of California, the Lawrence Berkeley Laboratory or the Department of Energy. Reference to a company or product name does not imply approval or recommendation of the product by the University of California or the U.S. Department of Energy to the exclusion of others that may be suitable.
This vacuum polarization displacement charge can be illustrated as in Fig. 5. Of particular inter... more This vacuum polarization displacement charge can be illustrated as in Fig. 5. Of particular interest to us here is the stripping-off of the vacuum polarization charge in case of the moving ions. This leads to the ejection of the e+e-pairs, which goes like (ZT + ZP) 20-power as a function of the colliding charges [1,2]. It has been observed experimentally by Backe, Kankeleit, et al. [3] and by Kienle, Greenberg, and associates [4]. 3. THE CHARGED VACUUM IN SUPERCRITICAL FIELDS If the charge of the central nucleus is increased, the spectrum looks for point and extended nuclei as in Fig. 6. For point nuclei the well-known fine-structure formula results, which has no solutions beyond Z = 137. This puzzle is postponed to the so-called critical charge Zcr-173 for extended nuclei, where the Is, state 'dives' into the negative continuum. For even higher central charge, a; "cr = 183 the Zp, state dives, etc. The significance of this is the following: In the overcritical 'case the dived bound state becomes degenerate with the (occupied) negative electron states. Hence spontaneous e'e-pair creation becomes possible, where an electron from the Dirac sea occupies the bound state, leaving a hole in a continuum state, which escapes as a positron. This is a fundamentally new process, which can also be expressed in the following way: The neutral vacuum of QED becomes unstable in overcritical electric fields. It decays in about 10-l' set into a charged vacuum. The charged vacuum is stable due to the Pauli principle. It is two times charged, because of the spin degeneracy two electrons (t,S) can occupy the dived shell. After the 2p+ shell dived beyond Zlcr = 183, the vacu
We derive the interaction of fermions with a dynamical space-time based on the postulate that the... more We derive the interaction of fermions with a dynamical space-time based on the postulate that the description of physics should be independent of the reference frame, which means to require the form-invariance of the fermion action under diffeomorphisms. The derivation is worked out in the Hamiltonian formalism as a canonical transformation along the line of non-Abelian gauge theories. This yields a closed set of field equations for fermions, unambiguously fixing their coupling to dynamical space-time. We encounter, in addition to the well-known minimal coupling, anomalous couplings to curvature and torsion. In torsion-free geometries that anomalous interaction reduces to a Pauli-type coupling with the curvature scalar via a spontaneously emerged new coupling constant with the dimension of mass resp. inverse length. A consistent model Hamiltonian for the free gravitational field and the impact of its functional form on the structure of the dynamical geometry space-time is discussed.
The Maxwell field can be viewed as a U (1)-gauge theory, therefore, generalizing it to forminvari... more The Maxwell field can be viewed as a U (1)-gauge theory, therefore, generalizing it to forminvariance in dynamical spacetime backgrounds should take this symmetry into account. This is of essential importance when generalizations of general relativity to theories with non-vanishing torsion are considered. Despite the many statements in literature that a U (1)-gauge field cannot couple to torsion, this issue was recently revived. In this letter we contribute to the discussion by demonstrating via a canonical transformation within the framework of the DeDonder-Weyl Hamiltonian formalism that a U (1)-gauge field does not couple to torsion.
In this letter, we show how a modification of the Einstein-Hilbert theory, namely the Covariant C... more In this letter, we show how a modification of the Einstein-Hilbert theory, namely the Covariant Canonical Gauge Gravity (CCGG), provides a comprehensive derivation of the cosmological constant and gives its correct order of magnitude. In CCGG a "deformation" of the Einstein-Hilbert Lagrangian of the free gravitational field by a quadratic Riemann-Cartan concomitant is required that is controlled by the ("deformation") parameter g 1. The field equations resulting from the variation of the action combine to an extended form of the Einstein field equation with an emergent cosmological constant Λ = 3M 2 p /2g 1. The deformation parameter has in preliminary cosmological (low red-shift) studies been shown to be consistent with g 1 ∼ 10 120 , providing a remarkably conclusive resolution of the cosmological constant problem.
The generic form of spacetime dynamics as a classical gauge field theory has recently been derive... more The generic form of spacetime dynamics as a classical gauge field theory has recently been derived, based on only the action principle and on the Principle of General Relativity. It was thus shown that Einstein's General Relativity is the special case where (i) the Hilbert Lagrangian (essentially the Ricci scalar) is supposed to describe the dynamics of the "free" (uncoupled) gravitational field, and (ii) the energy-momentum tensor is that of scalar fields representing real or complex structureless (spin-0) particles. It followed that all other source fields-such as vector fields representing massive and nonmassive spin-1 particles-need careful scrutiny of the appropriate source tensor. This is the subject of our actual paper: we discuss in detail the coupling of the gravitational field with (i) a massive complex scalar field, (ii) a massive real vector field, and (iii) a massless vector field. We show that different couplings emerge for massive and non-massive vector fields. The massive vector field has the canonical energy-momentum tensor as the appropriate source term-which embraces also the energy density furnished by the internal spin. In this case, the vector fields are shown to generate a torsion of spacetime. In contrast, the system of a massless and charged vector field is associated with the metric (Hilbert) energy-momentum tensor due to its additional U(1) symmetry. Moreover, such vector fields do not generate a torsion of spacetime. The respective sources of gravitation apply for all models of the dynamics of the "free" (uncoupled) gravitational field-which do not follow from the gauge formalism but must be specified based on separate physical reasoning.
International Journal of Modern Physics E-nuclear Physics, Jul 1, 2016
Electromagnetism, the strong and the weak interaction are commonly formulated as gauge theories i... more Electromagnetism, the strong and the weak interaction are commonly formulated as gauge theories in a Lagrangian description. In this paper we present an alternative formal derivation of U (1)-gauge theory in a manifestly covariant Hamilton formalism. We make use of canonical transformations as our guiding tool to formalize the gauging procedure. The introduction of the gauge field, its transformation behaviour and a dynamical gauge field Lagrangian/Hamiltonian are unavoidable consequences of this formalism, whereas the form of the free gauge Lagrangian/Hamiltonian depends on the selection of the gauge dependence of the canonically conjugate gauge fields.
An •interesting and until now unanswered question is how quarks, confined within a bag, interact ... more An •interesting and until now unanswered question is how quarks, confined within a bag, interact when their number is very large. , Can their residual interaction be understood in terms of perturbation theory or is it basically non-perturbative? As remote as any other possibility is to assume the quarks to be free within the bag, when the total baryon number corresponds to that of giant nuclei. We investigate here such giant quark bags with baryon numbers up to 1000. Experimental consequences and some spepulations in connection with the recently observed anomalous positron production are discussed. This report was done with support from the Department of Energy. Any conclusions or opinions expressed in this report represent solely those of the author(s) and not necessarily those of The Regents of the University of California, the Lawrence Berkeley Laboratory or the Department of Energy. Reference to a company or product name does not imply approval or recommendation of the product by the University of California or the U.S. Department of Energy to the exclusion of others that may be suitable.
This vacuum polarization displacement charge can be illustrated as in Fig. 5. Of particular inter... more This vacuum polarization displacement charge can be illustrated as in Fig. 5. Of particular interest to us here is the stripping-off of the vacuum polarization charge in case of the moving ions. This leads to the ejection of the e+e-pairs, which goes like (ZT + ZP) 20-power as a function of the colliding charges [1,2]. It has been observed experimentally by Backe, Kankeleit, et al. [3] and by Kienle, Greenberg, and associates [4]. 3. THE CHARGED VACUUM IN SUPERCRITICAL FIELDS If the charge of the central nucleus is increased, the spectrum looks for point and extended nuclei as in Fig. 6. For point nuclei the well-known fine-structure formula results, which has no solutions beyond Z = 137. This puzzle is postponed to the so-called critical charge Zcr-173 for extended nuclei, where the Is, state 'dives' into the negative continuum. For even higher central charge, a; "cr = 183 the Zp, state dives, etc. The significance of this is the following: In the overcritical 'case the dived bound state becomes degenerate with the (occupied) negative electron states. Hence spontaneous e'e-pair creation becomes possible, where an electron from the Dirac sea occupies the bound state, leaving a hole in a continuum state, which escapes as a positron. This is a fundamentally new process, which can also be expressed in the following way: The neutral vacuum of QED becomes unstable in overcritical electric fields. It decays in about 10-l' set into a charged vacuum. The charged vacuum is stable due to the Pauli principle. It is two times charged, because of the spin degeneracy two electrons (t,S) can occupy the dived shell. After the 2p+ shell dived beyond Zlcr = 183, the vacu
We derive the interaction of fermions with a dynamical space-time based on the postulate that the... more We derive the interaction of fermions with a dynamical space-time based on the postulate that the description of physics should be independent of the reference frame, which means to require the form-invariance of the fermion action under diffeomorphisms. The derivation is worked out in the Hamiltonian formalism as a canonical transformation along the line of non-Abelian gauge theories. This yields a closed set of field equations for fermions, unambiguously fixing their coupling to dynamical space-time. We encounter, in addition to the well-known minimal coupling, anomalous couplings to curvature and torsion. In torsion-free geometries that anomalous interaction reduces to a Pauli-type coupling with the curvature scalar via a spontaneously emerged new coupling constant with the dimension of mass resp. inverse length. A consistent model Hamiltonian for the free gravitational field and the impact of its functional form on the structure of the dynamical geometry space-time is discussed.
The Maxwell field can be viewed as a U (1)-gauge theory, therefore, generalizing it to forminvari... more The Maxwell field can be viewed as a U (1)-gauge theory, therefore, generalizing it to forminvariance in dynamical spacetime backgrounds should take this symmetry into account. This is of essential importance when generalizations of general relativity to theories with non-vanishing torsion are considered. Despite the many statements in literature that a U (1)-gauge field cannot couple to torsion, this issue was recently revived. In this letter we contribute to the discussion by demonstrating via a canonical transformation within the framework of the DeDonder-Weyl Hamiltonian formalism that a U (1)-gauge field does not couple to torsion.
In this letter, we show how a modification of the Einstein-Hilbert theory, namely the Covariant C... more In this letter, we show how a modification of the Einstein-Hilbert theory, namely the Covariant Canonical Gauge Gravity (CCGG), provides a comprehensive derivation of the cosmological constant and gives its correct order of magnitude. In CCGG a "deformation" of the Einstein-Hilbert Lagrangian of the free gravitational field by a quadratic Riemann-Cartan concomitant is required that is controlled by the ("deformation") parameter g 1. The field equations resulting from the variation of the action combine to an extended form of the Einstein field equation with an emergent cosmological constant Λ = 3M 2 p /2g 1. The deformation parameter has in preliminary cosmological (low red-shift) studies been shown to be consistent with g 1 ∼ 10 120 , providing a remarkably conclusive resolution of the cosmological constant problem.
The generic form of spacetime dynamics as a classical gauge field theory has recently been derive... more The generic form of spacetime dynamics as a classical gauge field theory has recently been derived, based on only the action principle and on the Principle of General Relativity. It was thus shown that Einstein's General Relativity is the special case where (i) the Hilbert Lagrangian (essentially the Ricci scalar) is supposed to describe the dynamics of the "free" (uncoupled) gravitational field, and (ii) the energy-momentum tensor is that of scalar fields representing real or complex structureless (spin-0) particles. It followed that all other source fields-such as vector fields representing massive and nonmassive spin-1 particles-need careful scrutiny of the appropriate source tensor. This is the subject of our actual paper: we discuss in detail the coupling of the gravitational field with (i) a massive complex scalar field, (ii) a massive real vector field, and (iii) a massless vector field. We show that different couplings emerge for massive and non-massive vector fields. The massive vector field has the canonical energy-momentum tensor as the appropriate source term-which embraces also the energy density furnished by the internal spin. In this case, the vector fields are shown to generate a torsion of spacetime. In contrast, the system of a massless and charged vector field is associated with the metric (Hilbert) energy-momentum tensor due to its additional U(1) symmetry. Moreover, such vector fields do not generate a torsion of spacetime. The respective sources of gravitation apply for all models of the dynamics of the "free" (uncoupled) gravitational field-which do not follow from the gauge formalism but must be specified based on separate physical reasoning.
International Journal of Modern Physics E-nuclear Physics, Jul 1, 2016
Electromagnetism, the strong and the weak interaction are commonly formulated as gauge theories i... more Electromagnetism, the strong and the weak interaction are commonly formulated as gauge theories in a Lagrangian description. In this paper we present an alternative formal derivation of U (1)-gauge theory in a manifestly covariant Hamilton formalism. We make use of canonical transformations as our guiding tool to formalize the gauging procedure. The introduction of the gauge field, its transformation behaviour and a dynamical gauge field Lagrangian/Hamiltonian are unavoidable consequences of this formalism, whereas the form of the free gauge Lagrangian/Hamiltonian depends on the selection of the gauge dependence of the canonically conjugate gauge fields.
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Papers by David Vasak