Help me make sense of this quantum universe

[QuantumDefect]

Hello I am a second year physics undergrad and I am still in the intro classes. I was wondering if someone could explain to me what all these fields entail and how they are related: Quantum Mechanics, Quantum Theory, and Quantum Field Theory. Thanks everyone for your responses.

 

[chroot]

'Quantum theory' is the umbrella term for any quantized (i.e. non-classical) theory. Quantum mechanics is the quantized version of classical mechanics, and is an example of a quantum theory. Quantum Field Theory is the name of a theory of particles in which every particle is a quantum of a field; i.e. the electron is the quantum of an electron field. Where the electron field is non-zero, we (may) perceive an electron. It is also an example of a quantum theory.

- Warren

 

[PRodQuanta]

Quantum Theory says energy isn't continuous, but is quantized. Quantum mechanics is the same thing, but of classical mechanics, and QFT... well... you drop a cat in a box and try and kill it with evil poison, without observing it...

I'm done with this comedy thing...

Paden Roder

 

[QuantumDefect]

I thought Quantum Mechanics was the study of matter and radiation at the atomic scale? wouldn't this include all of QFT?

 

[chroot]

Quantum mechanics is mechanics -- it deals with forces, motion, and so on. It does not deal directly with what the particles ARE, nor does it deal with the nature of how the forces work. QM does not deal directly with radiation -- that's the domain of a subdiscipline, quantum electrodynamics. Quantum field theory is the application of quantum mechanics to fields -- specifically, those representing particles.

- Warren

 

[dextercioby]

Classical particles are described at classical level by the coordinates q&p and the all important classical obervable called "Hamiltonian".Quantizing these 3 basic classical observables according to the second postulate of QM basically realizes the "quantization" of the system and therefore this theory is called Quantum MECHANICS.It's a quantized version of classical Hamilton mechanics,so it deals with the quantum observable called HAMILTONIAN (a densly defined self-adjoint linear operator) and with the concepts of operators for momentum,position,kinetic and potential energy,aso.
Classical fields (such as the electromagnetic field) are described by generally complex functions defined on the flat Minkowski space taking values in the algebra of either the real functions (the em field,the gluon field,the scalar boson field,the nonphysical Goldstone boson,the Higgs boson,...),complex functions (the complex scalar field) or in an exotic algebra called the Grassmann algebra (the (seminteger)spinor fields).All these fields are representations of the restricted Poincaré group,that is the group of space-time proper roto-translations.Each of these classical fields,when quantized accordingly to the second postulate,describes at quantum level a free relativistic particle with positive integer/seminteger spin.This is QFT.Then all u have to do is find appropriate interaction hamiltonians and build interactions between these particles...