Particle physics & QFT, A conceptual question

[gop]

Hi

In Halzen's "Quarks & Leptons" all discussed particle interactions conserve particle number in some sense (Actually particle number is not conserved but if you count the particles minus the antiparticles before the reaction you get the same "particles minus the antiparticles" number after the reaction. Which is in some sense particle conservation since in the Feynman
diagram antiparticles are particles that propagate backwards in time).

However, I'm not sure if this is the most general process possible in particle physics. Moreover, in this book and in some others I haven't seen an explicit approach to particle destruction and creation which exists (I think in form of "second quantization"). Nevertheless, those methods are identified with quantum field theory (and the standard model).

So I guess my question is how does particle physics, quantum field theory, and second quantization relate to each other.

thx

 

[javierR]

"Particle number" is not a generally conserved number.

Relativistic quantum mechanics is sometimes referred to as a "first quantized" theory. Quantum field theory is sometimes then called a "second quantized" theory (these expressions date back to the beginning of quantum mechanics and quantum field theory, and aren't useful descriptive labels). Particle physics refers to the study of elementary and composite particles and their interactions and can be formulated in either of the above frameworks: (relativistic) quantum mechanics or quantum field theory. In the first framework (followed often by intro particle physics) the objects are classical fields/potentials and particles/wavefunctions. In the second framework, the fundamental objects are all quantum fields, with particles and classical fields resulting from these; wavefunctions are then functionals of the quantum fields.

 

[RedX]

Hi

In Halzen's "Quarks & Leptons" all discussed particle interactions conserve particle number in some sense (Actually particle number is not conserved but if you count the particles minus the antiparticles before the reaction you get the same "particles minus the antiparticles" number after the reaction. Which is in some sense particle conservation since in the Feynman
diagram antiparticles are particles that propagate backwards in time).

However, I'm not sure if this is the most general process possible in particle physics.

As been mentioned, particle number is not conserved. For example, Brehmmstrahlung.

Particle minus antiparticle is conserved for fermions, but you're right to question it. It really has to do with the structure of the Dirac spinor, that it contains a particle and the conjugate of an antiparticle within it. If you build your interactions out of Dirac spinors, then it is inescapable that particles minus antiparticle is conserved. Obviously a Majorana spinor changes all that, which looks to be what a neutrino is really described by. So that particles minus antiparticles is conserved - looks like it's not true.

Moreover, in this book and in some others I haven't seen an explicit approach to particle destruction and creation which exists (I think in form of "second quantization"). Nevertheless, those methods are identified with quantum field theory (and the standard model).

The reason you're probably not seeing an approach like 2nd quantization in your book is because the book you're reading, by the title of it, is not a quantum field theory book, but a particle physics book.

 

[gop]

Hi

Thank you both for your answer. Maybe you can help me to clarify an additional point.

How does the standard model fits into this? The standard model is covered in most
particle physics books. So if it is a pretty complete description of nature (except gravity and neutrino mass of course) how can we understand e.g. things like Bremsstrahlung (where a photon is created or absorbed)?

thx

 

[humanino]

As been mentioned, particle number is not conserved. For example, Brehmmstrahlung.
[...]
The reason you're probably not seeing an approach like 2nd quantization in your book is because the book you're reading, by the title of it, is not a quantum field theory book, but a particle physics book.

Halzen and Martin goes far enough to describe scaling violation in QCD, which is essentially gluon Brehmmstrahlung. Maybe there is not the explicit sentence "caution : particle number is not conserved anymore in QFT", however, as early as paragraph 1.1 the fact that Schroedinger's equation can not describe the creation and annihilation of particle is discussed. Jet creation in electron-positron annihilation is depicted in 1.5

 

[RedX]

Hi

Thank you both for your answer. Maybe you can help me to clarify an additional point.

How does the standard model fits into this? The standard model is covered in most
particle physics books. So if it is a pretty complete description of nature (except gravity and neutrino mass of course) how can we understand e.g. things like Bremsstrahlung (where a photon is created or absorbed)?

thx

I can read a book about all the elements of the periodic table. The book can tell me the names of all the elements, their atomic weight, the # of electrons they have, some common reactions they're involved in, what minerals they're found in, how they were discovered historically, etc. But this doesn't mean I understand the chemistry behind all of it. For that I'd need to pick up a chemistry book. Chemistry explains the periodic table, and the periodic table summarizes all known elements.

It's the same with a particle physics book. It'll tell you a lot of information, but the physics behind it you'll get from picking up a quantum field theory book. Quantum field theory explains the Standard Model, and the Standard Model summarizes all known particles and forces.

 

[gop]

A final question. In what order does one approach these subjects up to know I thought first particle physics and then quantum field theory is the way to go. However, I'm not so sure anymore especially since (from looking at e.g. the TOC of Peskin, Schroeder "An Introduction To Quantum Field Theory") a lot of the topics and examples seems to be very similar and the book does list quantum mechanics as a prerequisit but does NOT mention particle physics as such.

thx

 

[humanino]

Particle physics is a narrower field than quantum mechanics. Particle physics requires the knowledge of quantum mechanics, and quantum field theory as well. Quantum mechanics is useful outside particle physics, and can be done without resorting to fields.

 

[Vanadium 50]

RedX is right that the Dirac structure of fermions forces (particle - antiparticle) to be conserved, but there is another reason: conservation of the various charges. If I make a red quark, somewhere in the system I must have also made an anti-red object as well. This effectively forces (particle - antiparticle) to be a conserved quantity.