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What is the difference between quantum mechanics and QFT?

  1. May 30, 2013 #1

    I'm an undergrad that has not taken quantum mechanics... What exactly is the distinction between quantum mechanics and quantum field theory? Does quantum mechanics describe the interactions of particles? Are Feynman diagrams used in quantum mechanics?

    I have been doing some reading over the internet and everything is starting to blur together... Also, if anyone can explain why Lie Algebra is used, that would be much appreciated...and why we need the Pauli matrices to form an orthogonal basis (why orthogonal?) in Hilbert Space (why not Euclidean?)

  2. jcsd
  3. May 30, 2013 #2
    I suggest you ask separate questions in different thread....
    For your main question, look at the first few pages of David Tong's QFT notes, under the section "Why Quantum Field Theory". Hope that helps.
  4. May 30, 2013 #3
    Thank you, I just took a quick look and read one sentence that is very helpful..

    "The primary reason for introducing the concept of the field is to construct laws of Nature which are local"...

    Appreciate it!
  5. May 30, 2013 #4


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    hi lonewolf219! :smile:
    QM is physics (including the maths tools necessary for the physics).

    QFT is a maths tool.

    Feynman diagrams are only used as part of QFT.
    In QM, everything has an amplitude.

    The probability is the amplitude times its complex conjugate.

    That means the amplitudes must be in a space with an inner product and a complex conjugate … we call that a Hilbert space. :wink:

    The different basis elements of a Hilbert space must be orthogonal (ie have inner product zero with each other). Making calculations would be impossibly long if we didn't express everything in terms of basis elements, that's why we need them.
  6. May 30, 2013 #5


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    Quantum field theory refers to several different theories were objects called "fields", obeying
    the laws of quantum mechanics, are used to model particle interactions.

    Quantum Mechanics can refer to any quantum theory. Sometimes it is used to specifically
    mean quantum theories which involve a fixed number of particles interacting with various classical potential energy distributions.

    For example, you can make a quantum mechanical model of hydrogen. Here the electron is quantum mechanical and the coloumb potential is classical.

    In a quantum field theory model of hydrogen, the electron is just a part of the electron field and the coloumb potential also results from the quantised photon field.

    Yes, to the first question. For the second question, yes they are, but not as commonly as the would be in quantum field theory.

    Lie algebras are just a certain type of algebra (vector spaces with a multiplication rule). They are important becuase they pop up in studying symmetries in quantum theories.

    The Pauli matricies are related to angular momentum, we need them when studying the spin of particles. We would want an orthogonal basis because it's mathematically much simpler, it seperates angular momentum into three mutually perpendicular directions.

    Quantum Mechanics uses Hilbert spaces, not Euclidean spaces.
  7. May 30, 2013 #6
    :smile:Great!!! Thank you very much! I wish I asked earlier!
  8. May 30, 2013 #7


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    I was too about to say something, but DarMM said it all. :biggrin:
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