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Definition/Summary Virtual particles are a mathematical device used in perturbation expansions of the S-operator (transition matrix) of interaction in quantum field theory. No virtual particle physically appears in the interaction: all possible virtual particles, and their antiparticles, occur equally and together in the mathematics and must be removed by integration over the values of their…
This Insight Article is a sequel to the Insight Article ”The Physics of Virtual Particles”, which contains an exposition of definitions that are physically justified, and in particular, makes precise what a virtual particle is and what being real means. As discussed in detail in the companion article, virtual particles are defined as (intuitive imagery…
In discussions on the internet (including a number of Wikipedia pages) and in books and articles for non-experts in particle physics, there is considerable confusion about various notions around the concept of particles of subatomic size, and in particular about the notion of a virtual particle. This is partly due to misunderstandings in the terminology…
There is an interesting story unfolding in particle physics. The main motivation for building the Large Hadron Collider was to search for new particles. And in July of 2012, the LHC found the Higgs boson, confirming the existence of this entirely new, but widely expected elementary particle. But the Higgs wasn’t the only particle most…
Abstract There is so much to say about the many endeavors by professional scientists to explain to us the world. The list is long: Carl Sagan, Harald Lesch, Neil deGrasse Tyson, Sabine Hossenfelder, Michio Kaku, and I even saw Roger Penrose and Steven Hawking on tv. The list is – of course – considerably longer…
This is one chapter in a series on Mathematical Quantum Field Theory. The previous chapter is 14. Free quantum fields. The next chapter is 16. Renormalization. 15. Interacting quantum fields In this chapter we discuss the following topics: Free field vacua Perturbative S-matrices Conceptual remarks Interacting field observables Time-ordered products (“Re”-)Normalization Feynman perturbation series Effective…
This Insight Article is a sequel of the Insight Articles ”The Physics of Virtual Particles”, “Misconceptions about Virtual Particles“ , and ”The Vacuum Fluctuation Myth”, which make precise what a virtual particle is, what being real means, document some of the liberties taken in physics textbooks in the use of this concept, mention the most…
This Insight Article is a sequel of the Insight Articles ”The Physics of Virtual Particles” and “Misconceptions about Virtual Particles“ which make precise what a virtual particle is and what being real means, document some of the liberties taken in physics textbooks in the use of this concept, and mention the most prominent misuses. A further…
Last time I sketched how physicists use quantum electrodynamics, or ‘QED’, to compute answers to physics problems as power series in the fine structure constant, which is $$ \alpha = \frac{1}{4 \pi \epsilon_0} \frac{e^2}{\hbar c} \approx \frac{1}{137.036} . $$ I concluded with a famous example: the magnetic moment of the electron. With a truly…
Quantum field theory is the best method we have for describing particles and forces in a way that takes both quantum mechanics and special relativity into account. It makes many wonderfully accurate predictions. And yet, it has embroiled physics in some remarkable problems: struggles with infinities! I want to sketch some of the…
Relativistic quantum field theory is notorious for the occurrence of divergent expressions that must be renormalized by recipes that on first sight sound very arbitrary and counterintuitive. But it doesn’t have to be this way… Traditional approaches The starting point of any quantum field theory is free fields that serve to define irreducible representations of…
Introduction In a previous Physics Forums article entitled “How to Master Projectile Motion Without Quadratics”, PF user @kuruman brought to our attention the vector equation ##\frac{|V_0 \times V_f|}{g} = R## and lamented the fact that: “Equally unused, untaught and apparently not even assigned as a “show that” exercise is Equation (4) that identifies the range as the…
Key Points Quantum mechanics is known for its strangeness, including phenomena like wave-particle duality, which allows particles to behave like waves. The double-slit experiment is a key demonstration of this duality, showing that even single particles, like photons, exhibit wave-like behavior. When the experiment measures which slit a particle goes through, it behaves like a…
We asked our PF Advisors “How do you see the rise in A.I. affecting STEM in the lab, classroom, industry and or in everyday society?”. We got so many great responses we need to split them into parts, here are the first several. This is part 3. Read part 1 here and part 2 here. Enjoy!…
We asked our PF Advisors to tell us their most memorable or influential textbook and why. Here are their responses… Thanks to all the PF Advisors that shared their favorite textbook. We have more questions for them in the near future. Stay tuned for another “Ask the Advisors”!
The terms Bizarro and Bizarro World originated in Superman comics, where strangely imperfect versions of Superman, other action characters, and even Earth itself were conceived of, and provided the basis of stories. And who can ever forget the Seinfeld episode entitled “Bizarro Jerry,” in which there are Bizarro versions of Jerry and all his friends?…
Please give us a brief background on yourself Over 40 years ago, I studied mathematics, physics and computer science in Freiburg and Berlin (Germany). My Ph.D. thesis was in pure mathematics, but I was later drawn more and more into applied mathematics. Since 1994 I am a full professor of mathematics at the University of…
The Connes-Lott-Chamseddine-Barrett model is the observation that the standard model of particle physics — as a classical action functional, but including its coupling to gravity and subsuming a fair bit of fine detail — may succinctly be encoded in terms of operator algebraic data called a “spectral triple”. This involves some non-commutative algebra, and…
Bayes’ Theorem: Balancing predictive success with falsifiability Despite its murky logical pedigree, confirmation is a key part of learning. After all, some of the greatest achievements of science are unabashed confirmations, from the discovery of acquired immunity to the gauge theory of particle physics. But because we cannot isolate a unique hypothesis from the…
We are proud to introduce you to Mathematical Physicist and PF member John Baez! Give us some background on yourself. I’m interested in all kinds of mathematics and physics, so I call myself a mathematical physicist. But I’m a math professor at the University of California in Riverside. I’ve taught here since 1989. My wife Lisa…