What is the significance of the kinetic term in a scalar field theory?

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SUMMARY

The kinetic term in a scalar field theory, represented by the action S=\int d^4x(\partial_\mu\phi\partial^\mu\phi), is fundamentally linked to the energy associated with the movement of the field. While it is often equated with kinetic energy, this interpretation can be misleading, especially for massless fields like photons. In classical mechanics, kinetic energy is defined as the energy due to motion, but for massless particles, energy is expressed as E=hν, leading to a nuanced understanding of kinetic energy in the context of relativistic physics. The relationship E=pc for massless particles further complicates the traditional view of kinetic energy.

PREREQUISITES
  • Understanding of scalar field theory
  • Familiarity with the action principle in physics
  • Basic knowledge of relativistic energy-momentum relations
  • Concept of kinetic energy in classical mechanics
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robousy
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I've been wondering about terms you typically find in the action of a field theory, for example consider the kinetic term of a scalar field

S=\int d^4x(\partial_\mu\phi\partial^\mu\phi).

I've read that it can be thought of as the kinetic energy of the field - but this just doesn't sit to well with me for some reason. I mean the kinetic energy of a massless field seems strange.

Can anyone here provide any deeper insights into this?
 
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does a photon has kinetic energy?
 
mjsd is right

think the definition (classically also) of what K is?

roughly speaking is the amount of energy that a system has, due just to his movement.

massles particles do move always at c.
 
hmmm... well I know that a photon has energy E=h\nu, but I've never called it knietic energy - but I see what you are getting at.
 
robousy said:
hmmm... well I know that a photon has energy E=h\nu, but I've never called it knietic energy - but I see what you are getting at.

rember also that for m=0 E=pc
 

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