- “When the multiverse and many-worlds collide” by Justin Mullins (The New Scientist; 2011.06.01) – http://www.newscientist.com/article/mg21028154.200-when-the-multiverse-and-manyworlds-collide.html
- “Are Many Worlds and the Multiverse the Same Idea?” by Sean Carroll (Cosmic Variance blog at Discover Magazine; ) – http://blogs.discovermagazine.com/cosmicvariance/2011/05/26/are-many-worlds-and-the-multiverse-the-same-idea/
- “Physical Theories, Eternal Inflation, and Quantum Universe” by Yasunori Nomura (arXiv.org > hep-th > arXiv:1104.2324v2 [hep-th])- http://arxiv.org/abs/1104.2324
- Abstract:

*We present a framework in which well-defined predictions are obtained in an eternally inflating multiverse, based on the principles of quantum mechanics. We show that the entire multiverse is described purely from the viewpoint of a single “observer,” who describes the world as a quantum state defined on his/her past light cones bounded by the (stretched) apparent horizons. We find that quantum mechanics plays an essential role in regulating infinities. The framework is “gauge invariant,” i.e. predictions do not depend on how spacetime is parametrized, as it should be in a theory of quantum gravity. Our framework provides a fully unified treatment of quantum measurement processes and the multiverse. We conclude that the eternally inflating multiverse and many worlds in quantum mechanics are the same. Other important implications include: global spacetime can be viewed as a derived concept; the multiverse is a transient phenomenon during the world relaxing into a supersymmetric Minkowski state. We also present a theory of “initial conditions” for the multiverse. By extrapolating our framework to the extreme, we arrive at a picture that the entire multiverse is a fluctuation in the stationary, fractal “mega-multiverse,” in which an infinite sequence of multiverse productions occurs. The framework discussed here does not suffer from problems/paradoxes plaguing other measures proposed earlier, such as the youngness paradox, the Boltzmann brain problem, and a peculiar “end” of time.* - “The Multiverse Interpretation of Quantum Mechanics” by Raphael Bousso and Leonard Susskind (arXiv.org > hep-th > arXiv:1105.3796v1 [hep-th]) – http://arxiv.org/abs/1105.3796
- Abstract:

*We argue that the many-worlds of quantum mechanics and the many worlds of the multiverse are the same thing, and that the multiverse is necessary to give exact operational meaning to probabilistic predictions from quantum mechanics.*

Decoherence – the modern version of wave-function collapse – is subjective in that it depends on the choice of a set of unmonitored degrees of freedom, the “environment”. In fact decoherence is absent in the complete description of any region larger than the future light-cone of a measurement event. However, if one restricts to the causal diamond – the largest region that can be causally probed – then the boundary of the diamond acts as a one-way membrane and thus provides a preferred choice of environment. We argue that the global multiverse is a representation of the many-worlds (all possible decoherent causal diamond histories) in a single geometry.

We propose that it must be possible in principle to verify quantum-mechanical predictions exactly. This requires not only the existence of exact observables but two additional postulates: a single observer within the universe can access infinitely many identical experiments; and the outcome of each experiment must be completely definite. In causal diamonds with finite surface area, holographic entropy bounds imply that no exact observables exist, and both postulates fail: experiments cannot be repeated infinitely many times; and decoherence is not completely irreversible, so outcomes are not definite. We argue that our postulates can be satisfied in “hats” (supersymmetric multiverse regions with vanishing cosmological constant). We propose a complementarity principle that relates the approximate observables associated with finite causal diamonds to exact observables in the hat.

## 2011.06.03

### Decoherence

## 2011.02.11

### Vacuum energy

- “Vacuum has friction after all” by David Harris (New Scientist, issue 2799; 2011.02.11) – http://www.newscientist.com/article/mg20927994.100-vacuum-has-friction-after-all.html
- Asymmetric interaction of a rotating object with the virtual photons moving in the same direction (as objects rotation) vs the ones moving in the opposite direction provides loss of angular momentum, i.e. effective friction

- “Vacuum has friction after all” by Deskarati (2011.02.11) – http://deskarati.com/2011/02/11/vacuum-has-friction-after-all/

## 2011.01.02

### Exact solutions

- “Mass generation and supersymmetry” by Marco Frasca (arXiv:1007.5275; 2010.12.26) – http://arxiv.org/abs/1007.5275
- Abstract:

*Using a recent understanding of mass generation for Yang-Mills theory and a quartic massless scalar field theory mapping each other, we show that when such a scalar field theory is coupled to a gauge field and Dirac spinors, all fields become massive at a classical level with all the properties of supersymmetry fulfilled, when the self-interaction of the scalar field is taken infinitely large. Assuming that the mechanism for mass generation must be the same in QCD as in the Standard Model, this implies that Higgs particle must be supersymmetric.* - “Exact solutions of classical scalar field equations” by Marco Frasca (arXiv:0907.4053; 2009.07.23) – http://arxiv.org/abs/0907.4053
- Abstract:

*We give a class of exact solutions of quartic scalar field theories. These solutions prove to be interesting as are characterized by the production of mass contributions arising from the nonlinear terms while maintaining a wave-like behavior. So, a quartic massless equation has a nonlinear wave solution with a dispersion relation of a massive wave and a quartic scalar theory gets its mass term renormalized in the dispersion relation through a term depending on the coupling and an integration constant. When spontaneous breaking of symmetry is considered, such wave-like solutions show how a mass term with the wrong sign and the nonlinearity give rise to a proper dispersion relation. These latter solutions do not change the sign maintaining the property of the selected value of the equilibrium state. Then, we use these solutions to obtain a quantum field theory for the case of a quartic massless field. We get the propagator from a first order correction showing that is consistent in the limit of a very large coupling. The spectrum of a massless quartic scalar field theory is then provided. From this we can conclude that, for an infinite countable number of exact classical solutions, there exist an infinite number of equivalent quantum field theories that are trivial in the limit of the coupling going to infinity.*

## 2010.07.13

### Time inversion

Time inversion

## Scalar field – real

where .

So:

## Scalar field – complex

## Dirac field

Here:

where

Then

\ni where .

Now

Split s/t

Their realizations are:

## Electromagnetic field

- .

## 2010.05.30

### String-inspired methods

- Worldline formalism – http://www.physics.thetangentbundle.net/wiki/Quantum_field_theory/worldline_formalism
- V.A. Fock (1937).
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*Phys. Rev.***84**: 108. - Julian Schwinger (1951). – On Gauge Invariance and Vacuum Polarization“.
*Phys. Rev.*: 664-679. | download: http://www.physics.princeton.edu/~mcdonald/examples/QED/schwinger_pr_82_664_51.pdf - L. Brink, P. Di Vecchia and P. Howe (1977). “Lagrangian Formulation of the Classical and Quantum Dynamics of Spinning Particles”.
*Nucl. Phys. B***118**: 76. - F. A. Berezin and M. S. Marinov (1975). – Classical spin and Grassmann algebra“.
*JETP Lett.***21**: 320. - R. Casalbuoni (1976). – The classical mechanics for Bose-Fermi systems“.
*Nuovo Cimento A***33**: 389. - F. Bastianelli (2005). – Worldline approach to vector and antisymmetric tensor fields“.
*JHEP***0504**. | arXiv: hep-th/0503155. - F. Bastianelli (2005). – Worldline approach to vector and antisymmetric tensor fields. II.“.
*JHEP***0510**. | arXiv: hep-th/0510010. - Ryusuke Endo. – Gauge Dependence of the Grabvitational Conformal Anomaly for the Electromagnetic Field“.
*Prog.Theor.Phys.***71**: 1366-1984. - Kim Milton (ed.), Giuseppe Bimonte, Enrico Calloni, Luciano Di Fiore, Giampiero Esposito, Leopoldo Milano, Luigi Rosa (2004).

“Photon Green Functions in Curved Space-Time”,.

Published in Quantum Field Theory Under the Influence of External Conditions: Proceedings

Rinton Press, 358-363. ISBN 1-58949-033-9. - V O Rivelles, L Sandoval Jr (1991). – BRST quantization of relativistic spinning particles with a Chern-Simons term“.
*Class. Quantum Grav.***8**: 1605-1612. - M. Reuter, M. G. Schmidt, C. Schubert (1997). – Constant External Fields in Gauge Theory and the Spin 0, 1/2, 1 Path Integrals“.
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*Phyz. Z. Sow.***12**: 404â€“425. - Christian Schubert (2001). “Perturbative Quantum Field Theory in the String-Inspired Formalism”.
*Phys.Rept.***355**: 73-234. arXiv: hep-th/0101036v2. - Christian Schubert. “QED in the worldline representation”. arXiv: hep-th/0703186v2.
- Z. Bern, D.A. Kosower (1991). – Color decomposition of one-loop amplitudes in gauge theories“.
*Nucl. Phys. B***362**: 389. - Z. Bern, D.A. Kosower (1992). – The computation of loop amplitudes in gauge theories“.
*Nucl. Phys. B***379**: 451. - M.J. Strassler (1992). “Field theory without Feynman diagrams: One-loop effective actions”.
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- V.A. Fock (1937).
- “The higher derivative expansion of the effective action by the string-inspired method. I” by Denny Fliegner, Michael G. Schmidt and Christian Schubert – http://www.springerlink.com/content/q8q455v2637w23u7/ (access for pay); Zeitschrift fÃ¼r Physik C (Particles and Fields); Springer; ISSN 0170-9739 (Print) 1431-5858 (Online); Issue Volume 64, Number 1 / March, 1994; Pages 111-116; Thursday, May 12, 2005
*Abstract The higher derivative expansion of the one-loop effective action for an external scalar potential is calculated to order {ie111-1}, using the string-inspired Bern-Kosower method in the first quantized path integral formulation. Comparisons are made with standard heat kernel calculations and with the corresponding Feynman diagrammatic calculation in order to show the efficiency of the present method.*free access to pre-print at arXiv: http://arxiv.org/abs/hep-ph/9401221

- “Trace anomalies and the string-inspired definition of quantum-mechanical path integrals in curved space” by K. Schalm, P. van Nieuwenhuizen; 15 Oct 1998 – http://arxiv.org/abs/hep-th/9810115
*Abstract: We consider quantum-mechanical path integrals for non-linear sigma models on a circle defined by the string-inspired method of Strassler, where one considers periodic quantum fluctuations about a center-of-mass coordinate. In this approach one finds incorrect answers for the local trace anomalies of the corresponding $n$-dimensional field theories in curved space. The quantum field theory approach to the quantum-mechanical path-integral, where quantum fluctuations are not periodic but vanish at the endpoints, yields the correct answers. We explain these results by a detailed analysis of general coordinate invariance in both methods. Both approaches can be derived from the same operator expression and the integrated trace anomalies in both schemes agree. In the string-inspired method the integrands are not invariant under general coordinate transformations and one is therefore not permitted to use Riemann normal coordinates.* - “The Structure of the Bern-Kosower Integrand for the N-Gluon Amplitude” by Christian Schubert – http://arxiv.org/abs/hep-th/9710067
*An ambiguity inherent in the partial integration procedure leading to the Bern-Kosower rules is fixed in a way which preserves the complete permutation symmetry in the scattering states. This leads to a canonical version of the Bern-Kosower representation for the one-loop N – photon/gluon amplitudes, and to a natural decomposition of those amplitudes into permutation symmetric gauge invariant partial amplitudes. This decomposition exhibits a simple recursive structure.* - “Bern-Kosower rule for scalar QED” by K Daikouji (1996) – http://ir.library.tohoku.ac.jp/re/bitstream/10097/35282/1/p4598_1.pdf