scholarly journals Probability Calculations Within Stochastic Electrodynamics

2021 ◽  
Vol 8 ◽  
Author(s):  
Daniel C. Cole
Keyword(s):  
Electromagnetic Fields ◽  
First Principles ◽  
Quantum Electrodynamics ◽  
Zero Point ◽  
Probability Density Functions ◽  
Integral Approach ◽  
Multiple Points ◽  
Stochastic Electrodynamics ◽  
Dipole Oscillator ◽  
Weighted Paths

Several stochastic situations in stochastic electrodynamics (SED) are analytically calculated from first principles. These situations include probability density functions, as well as correlation functions at multiple points of time and space, for the zero-point (ZP) electromagnetic fields, as well as for ZP plus Planckian (ZPP) electromagnetic fields. More lengthy analytical calculations are indicated, using similar methods, for the simple harmonic electric dipole oscillator bathed in ZP as well as ZPP electromagnetic fields. The method presented here makes an interesting contrast to Feynman’s path integral approach in quantum electrodynamics (QED). The present SED approach directly entails probabilities, while the QED approach involves summing weighted paths for the wave function.

scholarly journals Energy Considerations of Classical Electromagnetic Zero-Point Radiation and a Specific Probability Calculation in Stochastic Electrodynamics

Atoms ◽  
2019 ◽  
Vol 7 (2) ◽  
pp. 50
Author(s):  
Daniel C. Cole
Keyword(s):  
Radiation Field ◽  
Quantum Electrodynamics ◽  
Zero Point ◽  
New Method ◽  
Stochastic Electrodynamics ◽  
Probability Calculation

The zero-point (ZP) radiation field in stochastic electrodynamics (SED) is considered to be formally infinite, or perhaps bounded by mechanisms yet to be revealed someday. A similar situation holds in quantum electrodynamics (QED), although there the ZP field is considered to be “virtual”. The first part of this article addresses the concern by some about the related disturbing concept of “extracting energy” from this formally, enormous source of energy. The second part of this article introduces a new method for calculating probabilities of fields in SED, which can be extended to linear oscillators in SED.

scholarly journals If the propagator of QED were reversed, the mathematics of Nature would be much simpler

2020 ◽  
Vol 18 ◽  
pp. 129-153
Author(s):  
Jeffrey Boyd
Keyword(s):  
Wave Function ◽  
Path Integral ◽  
Quantum Electrodynamics ◽  
Probability Amplitude ◽  
Integral Approach ◽  
Everyday Experience ◽  
Wave Function Collapse ◽  
Path Integral Approach ◽  
Classical World ◽  
The Many

In Quantum ElectroDynamics (QED) the propagator is a function that describes the probability amplitude of a particle going from point A to B. It summarizes the many paths of Feynman’s path integral approach. We propose a reverse propagator (R-propagator) that, prior to the particle’s emission, summarizes every possible path from B to A. Wave function collapse occurs at point A when the particle randomly chooses one and only one of many incident paths to follow backwards with a probability of one, so it inevitably strikes detector B. The propagator and R-propagator both calculate the same probability amplitude. The R-propagator has an advantage over the propagator because it solves a contradiction inside QED, namely QED says a particle must take EVERY path from A to B. With our model the particle only takes one path. The R-propagator had already taken every path into account. We propose that this tiny, infinitesimal change from propagator to R-propagator would vastly simplify the mathematics of Nature. Many experiments that currently describe the quantum world as weird, change their meaning and no longer say that. The quantum world looks and acts like the classical world of everyday experience.

scholarly journals WORLDSHEET COVARIANT PATH INTEGRAL QUANTIZATION OF STRINGS

2006 ◽  
Vol 21 (32) ◽  
pp. 6525-6574 ◽  
Author(s):  
ANDRÉ VAN TONDER
Keyword(s):  
Path Integral ◽  
First Principles ◽  
Critical Dimension ◽  
Functional Integral ◽  
Integral Approach ◽  
Vertex Operators ◽  
General Covariance ◽  
Classical Transformation ◽  
Definition Of ◽  
Independent Path

We discuss a covariant functional integral approach to the quantization of the bosonic string. In contrast to approaches relying on noncovariant operator regularizations, interesting operators here are true tensor objects with classical transformation laws, even on target spaces where the theory has a Weyl anomaly. Since no implicit noncovariant gauge choices are involved in the definition of the operators, the anomaly is clearly separated from the issue of operator renormalization and can be understood in isolation, instead of infecting the latter as in other approaches. Our method is of wider applicability to covariant theories that are not Weyl invariant, but where covariant tensor operators are desired. After constructing covariantly regularized vertex operators, we define a class of background-independent path integral measures suitable for string quantization. We show how gauge invariance of the path integral implies the usual physical state conditions in a very conceptually clean way. We then discuss the construction of the BRST action from first principles, obtaining some interesting caveats relating to its general covariance. In our approach, the expected BRST related anomalies are encoded somewhat differently from other approaches. We conclude with an unusual but amusing derivation of the value D = 26 of the critical dimension.

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