Quantum field theory

[chandragupta]

Is it true that the universe is filled with all the different kinds of fundamental particles I.e. quanta waiting to be thought of by the observer & then waiting to be measured first Mathematically & then experimentally by the observer-------this is what is a FIELD THEORY. Your thoughts?

[derek w]

No,I think your looking at it wrong.

[ajb]

A field theory is "just" an assignment of a mathematical object to all point of space-time. In quantum field theory one attaches to every point in space-time fields whose quanta are the particles and forces we all know and love.

[chandragupta]

Quantum field theory is an amazing Mathematical invention of man's mind invented to make sense of this amazing universe. In this theory space-time at any given moment of its evolution is pictured as occupied by point-like characters having only charge but no mass with the exception of photons which are inherently without charge & without mass. Each of these point-like characters with charge generate their own individual electromagnetic field & thus interact with each other depending upon the nature of their charge (+or-),either attracting or repelling,thus creating newer & newer point-like characters with charges of different amplitudes (amplitudes which are different from the amplitudes of the original point-like characters from which they were made).

[chandragupta]

Motion of an individual quantum can take place in left to right & right to left direction in the form of an oscillation.central point on this arc of oscillation is called the point of equilibrium or rest & it denotes having zero charge. Photon is the point of energy at this site of equilibrium & thus having no charge. When this point of energy oscillates to the left of the site of equilibrium,it becomes electron with negative charge & if it oscillates to the right of the site of equilibrium, it becomes positron with positive(+) charge. But this is not the end of the story. This Mathematical point of energy can also move in an up & down fashion in a four dimensional space-time but when they move up & down, they do this in the form of a wave & not in a straight line. What energy- characteristic this point of energy I.e. quantum, acquires by moving in a wave like manner, I shall attempt to describe in lesson no 3. Your thoughts?

[chandragupta]

Quantum field theory, even though it is a theory, has a solid mathematical foundation which works splendedly in practice in real clasical world .Mathematics,even though an invention of man's mind & an abstract construct is nevertheless picturized by man for the purposes of ease of understanding, in a four dimensional space time,even if this happens to be quanta's infinitesimally small four dimensional space time. So my question is:- Is this Hilbert space,abstract though it is, by being a part of abstract mathematics , is nevertheless a micro four dimensional space time where quanta are points of energy having minuscule electromagnetic fields?£ Their quantum motion has to be expressed in abstract Mathematical terms because they are points of energy operating in infinitesimally small four dimensional spase time.Thus their wave function is not a wave function in the clasical sense but described as amplitude of probability & oscillations as a movement from negative point to a positive point through a point of equilibrium at zero. Thus a photon can be thought of as an oscillation from negative to positive point about the point of equilibrium. In this picturization electron can be considered on the negative side of equilibrium & positron on the positive side of the equilibrium . Your thoughts?

[juanrga]

Quantum field theory, even though it is a theory, has a solid mathematical foundation

 

At contrary QFT lacks any sound mathematical foundation. The theory is more as a collection of recipes which are forced to work for predetermined problems using certain tricks as renormalization, regularization and so on. Attempts to give QFT a solid mathematical foundation are stagnat.

 

http://en.wikipedia.org/wiki/Quantum_field_theory#Axiomatic_approaches

 

http://en.wikipedia.org/wiki/Axiomatic_quantum_field_theory

 

So my question is:- Is this Hilbert space,abstract though it is, by being a part of abstract mathematics , is nevertheless a micro four dimensional space time where quanta are points of energy having minuscule electromagnetic fields?£ Their quantum motion has to be expressed in abstract Mathematical terms because they are points of energy operating in infinitesimally small four dimensional spase time.

 

No. The Hilbert space used in QFT is completely unrelated to spacetime. The Hilbert space is where state functions (Dirac kets) live (there is no wavefunctions in QFT). The dimension of the Hilbert space is not four, but varies with the basis used. It is ordinary to work with infinite-dimensional Hilbert spaces.