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Reply to "Comment on 'Fermion production in a magnetic field in a de Sitter universe"'

Cosmin Crucean, Mihaela-Andreea Băloi
2017 Physical Review D  
In this paper we study the problem of gauge invariance of the first order transition amplitudes in de Sitter QED in Coulomb gauge.  ...  D95, are not directly applicable to the results in our paper since their proposed gauge transformations do not preserve the Coulomb gauge.  ...  Acknowledgements We would like to thank to Professor L. H. Ford for his observations that help us to improve our paper. We would also like to thank Professor Ion Cotȃescu, Dr. Victor Ambruş  ... 
doi:10.1103/physrevd.95.048502 fatcat:ge4pz5bfu5euni6o7je3mrudve

Lorentz and CPT violations in QED : a short comment on recent controversies [article]

Guy Bonneau
2001 arXiv   pre-print
We rediscuss the recent controversy on a possible Chern-Simons like term generated through radiative corrections in QED with a CPT violating term.  ...  We emphasize the fact that any absence of an a priori divergence should be explained by some symmetry or some non-renormalisation theorem : otherwise, no prediction can be made on the corresponding quantity  ...  -It is difficult to see the difference often advocated between a first order (in b µ ) perturbative calculation and what is claimed to be a "non-perturbative unambiguous value", but is, as a matter of  ... 
arXiv:hep-th/0109105v2 fatcat:jhyf4tpfvjdlfm62mpfm4ppshm

The QED Manifesto after Two Decades - Version 2.0

Ittay Weiss
2016 Journal of Software  
The QED 2.0 project will be a major scientific undertaking requiring the cooperation and efforts of hundreds of mathematicians, considerable ingenuity by many computer scientists, and a careful analysis  ...  "QED is the very tentative title of a project to build a computer system that effectively represents all important mathematical knowledge and techniques.  ...  Acknowledgment The author is grateful to Rahel Berman for clarifying conversations on the subject matter of this article.  ... 
doi:10.17706/jsw.11.8.803-815 fatcat:s4tvqzfbirf4nlhhjdb6on7pcm

Structured Proofs in Isar/HOL [chapter]

Tobias Nipkow
2003 Lecture Notes in Computer Science  
This paper is an introduction to the basic constructs of this language.  ...  Acknowledgement I am deeply indebted to Markus Wenzel for conceiving Isar.  ...  Note that it remains implicit what the two cases are: it is merely expected that the two subproofs prove P =⇒ ?thesis and ¬P =⇒ ?thesis (in that order) for some P.  ... 
doi:10.1007/3-540-39185-1_15 fatcat:vgrcqdg6szdotg7dqd3eb3lno4

Mixing Computations and Proofs

Michael Beeson
2014 Journal of Formalized Reasoning  
We compare the various approaches to proofs with a significant computational component, including (i) verifying the algorithms, (ii) verifying the results of the unverified algorithms, and (iii) trusting  ...  an external computation.  ...  The "reason" is many thousands of lines of proof and computation; if it can be shortened to digestible size, that remains for a future generation.  ... 
doi:10.6092/issn.1972-5787/4552 dblp:journals/jfrea/Beeson16 fatcat:ieften5wunhnnesihejategbku

Proof assistants: History, ideas and future

H. Geuvers
2009 Sadhana (Bangalore)  
An important application is and will be in computer supported modelling and verification of sys tems.  ...  In this paper I will discuss the fundamental ideas behind proof assis tants: What are they and what is a proof anyway?  ...  In this respect it is instructive to read what the authors of the QED manifesto thought that needed to be done.  ... 
doi:10.1007/s12046-009-0001-5 fatcat:nnrgwwfdxjhqnfdoye7s4665su

Improving QED-Tutrix by Automating the Generation of Proofs

Ludovic Font, Philippe R. Richard, Michel Gagnon
2018 Electronic Proceedings in Theoretical Computer Science  
QED-Tutrix offers an interesting approach to geometry education, but is currently crippled by the lengthiness of the process of implementing new problems, a task that must still be done manually.  ...  by the teacher, and 4) to be able to help the student at any step of the resolution of the problem, if the need arises.  ...  In Section 2, we present systems similar to QED-Tutrix, and also existing tools for automated theo- rem proving that could be useful for the task of generating proofs.  ... 
doi:10.4204/eptcs.267.3 fatcat:ltk6vod4ezdgzfiy23axok6foy

Struggles with the Continuum [article]

John C. Baez
2020 arXiv   pre-print
Our assumption that spacetime is a continuum leads to many challenges in mathematical physics.  ...  In general relativity, singularities are intimately connected to some of the theory's most dramatic successful predictions.  ...  If so, the remaining question would be why it takes so much work to prove this, and thus prove that Newtonian gravity makes definite predictions in almost all cases.  ... 
arXiv:1609.01421v4 fatcat:y24pfvtpezeztb7yj47zuu4lx4

From operational to denotational semantics [chapter]

Scott F. Smith
1992 Lecture Notes in Computer Science  
In this paper it is shown how operational semantic methods may be naturally extended to encompass many of the concepts of denotational semantics.  ...  Furthermore, it is not necessary to construct the cpo, for principles such as soundness of xed-point induction may be obtained by direct reasoning from this new ordering.  ...  Acknowledgements I owe many thanks to Carolyn Talcott for important suggestions and comments. Thanks also to Albert Meyer for useful comments.  ... 
doi:10.1007/3-540-55511-0_3 fatcat:rsl5dp26mfffvef4yqpnde2m7e

Automating the Generation of High School Geometry Proofs using Prolog in an Educational Context

Ludovic Font, Sébastien Cyr, Philippe R. Richard, Michel Gagnon
2020 Electronic Proceedings in Theoretical Computer Science  
This can only be done by knowing, beforehand, the possible ways to solve a problem. Hence the need for an automated theorem prover that provide proofs as they would be written by a student.  ...  To achieve this objective, logic programming is a natural tool due to the similarity of its reasoning with a mathematical proof by inference.  ...  For this behavior to be possible, the "valid but useless" elements must remain in the graph and be identified as such.  ... 
doi:10.4204/eptcs.313.1 fatcat:jukzspwlqrhcdlhwgthyceb4ji

Teaching Formal Methods and Discrete Mathematics

Mathieu Jaume, Théo Laurent
2014 Electronic Proceedings in Theoretical Computer Science  
To make the task easier, providing tools that help during the development cycle is essential but we think that education of computer scientists and software engineers is also an important challenge to  ...  In this paper, we claim that teaching formal methods could be done at the undergraduate level by mixing formal methods and discrete mathematics courses and we illustrate such an approach with a small develop  ...  Acknowledgments The authors would like to thank Renaud Rioboo for his help and for enlightening discussions about how to program with FoCaLiZe and about teaching discrete mathematics.  ... 
doi:10.4204/eptcs.149.4 fatcat:skw7camyfjh3fhmpmzjqm2sbay

Extended QED with CPT violation: Clarifying some controversies

Guy Bonneau
2007 Nuclear Physics B  
We rediscuss the controversy on a possible Chern-Simons like term generated through radiative corrections in QED with a CPT violating term.  ...  We also emphasize the fact that any absence of an a priori divergence should be explained by some symmetry or some non-renormalisation theorem and show that the so-called "unambiguous result" based upon  ...  However, as soon as PCAC is used to compute the decay Π 0 → γ γ , this triangle graph has to be computed and gauge invariance of the unintegrated three-vertices function is required.  ... 
doi:10.1016/j.nuclphysb.2006.11.028 fatcat:uftkiqxtv5d5roc64ptfrbeuqe

THE EULER-HEISENBERG LAGRANGIAN BEYOND ONE LOOP

IDRISH HUET, MICHEL RAUSCH DE TRAUBENBERG, CHRISTIAN SCHUBERT
2012 International Journal of Modern Physics, Conference Series  
We review what is presently known about higher loop corrections to the Euler-Heisenberg Lagrangian and its Scalar QED analogue.  ...  As a further step in a long-term effort to prove or disprove the convergence of the N photon amplitudes in the quenched approximation, we present a parameter integral representation of the three-loop Euler-Heisenberg  ...  The purpose of this talk is to give a summary on what is known about the EHL at the multiloop level, and to argue that those multiloop corrections, although not likely to be of phenomenological interest  ... 
doi:10.1142/s2010194512007507 fatcat:yg44fpoqevdihl424ms4xk2uhu

Hammering towards QED

Jasmin C. Blanchette, Cezary Kaliszyk, Lawrence C. Paulson, Josef Urban
2014 Journal of Formalized Reasoning  
We also discuss the relation of this technology to the QED Manifesto and consider its implications for QED-style efforts.  ...  This paper surveys the emerging methods to automate reasoning over large libraries developed with formal proof assistants. We call these methods hammers.  ...  Given a conjecture c and a fact f , naive Bayes computes the probability of f being needed to prove c, based on the previous use of f in proving conjectures that are similar to c.  ... 
doi:10.6092/issn.1972-5787/4593 dblp:journals/jfrea/BlanchetteKPU16 fatcat:zw4fz3wjrbfm3acuk4f576mzxm

Spin and orbital angular momentum in gauge theories (I): QED and determination of the angular momentum density [article]

X.S. Chen, X.F. Lü, W.M. Sun, F. Wang, T. Goldman
2007 arXiv   pre-print
This QED part reveals: 1) The spin and orbital angular momenta of electrons and photons can all be consistently defined gauge invariantly. 2) These gauge-invariant quantities can be conveniently computed  ...  The QCD paper [arXiv:0907.1284] will give a non-trivial generalization to non-Abelian gauge theories, and discuss the connection to nucleon spin structure.  ...  (8) can all be conveniently computed via the canonical operators in the Coulomb gauge.  ... 
arXiv:0709.3649v1 fatcat:krhq2ag5yjg4lktsh4qomzphfm
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