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Why Second Quantization?

  1. Mar 3, 2004 #1
    The quantum theory of field is sometimes known as second quantization.

    There are two distinct types of field in physics:

    1. Scalar field.
    2. Vector field.

    For each field, a force is supposed to be associated with it. But for the scalar field, this force is zero. This zero-force destroys the built-in sense of "direction" for the field.

    There were four known fields before Standard Model. These are the EM field, the strong field, the weak field, and the gravity field. All these are agreed to be vector fields with their respective quanta as the photon, the gluon, the W's and Z, and the graviton. The integral spins of these quanta make them bosons. But the graviton is a much more complicated vector (tensor) boson because its spin is 2.

    After the Standard Model, a new type of scalar field is formulated in physics. This is the Higgs field. The parameter for this field is the mass. Mass is a scalar quantity. It has no sense of direction.

    Both graviton and Higgs boson are yet to be found.

    The graviton has zero mass, while the Higgs boson is theorized to be a very heavy boson. The concept of mass is explicitly stated in only two force equations in physics: Newton's 2nd law of motion (inertial force) and his law of universal gravitation (gravity force). Yet in Einstein's general relativity, these two mass-forces are equivalent.

    Both graviton and Higgs boson must somehow be connected at a deeper level. Say at the Planck scales of length, time, and energy.

    Maybe the graviton and the Higgs boson are just two different way of viewing the same fundamental particle of a quantized scalar field?
  2. jcsd
  3. Mar 7, 2004 #2
    The difficulties of detecting the graviton and the Higgs boson may be due to the fact that they are not really bosons but fermions.

    They are fermions in one universe. In order for them to become bosons, they must seek and interact with identical quanta in another parallel universe. If this assertion is true, then they can never be detected as an isolated particle in only one universe such as ours. The magnetic monopole falls into the same assertion except only that it's a boson seeking another identical boson in the parallel universe.
  4. Mar 7, 2004 #3
    At this point, I am going to make a confession.

    The title of this thread should have been the same as that of Michio Kaku's book called Quantum Field Theory: A Modern Introduction" chapter 1 'Why Quantum Field Theory?'.

    Since I just bought this book last Friday (Mar 5th), I am not aware that I should have made that title. It has been sitting on the shelf in the bookstore. I happen to see it while looking for some other book (A Catalog of Special Plane Curves by Lawrence).

    I seems to be working everything backward. first, I waited until there is a problem in my independent research before I go around looking for books that will help me clear things up. And it also seems that most of the major theoretical problems are already been solved and I am just wasting my time redoing everything. I know I am doing things the hard way but this is the only way that I can do for not having the opportunity of a good solid foundation in my college years.

    When I bought this book by Kaku, I also bought the one by Dirac. A 4th edition of "The principle of Quantum Mechanics." Both of them were sitting on the bookshelf side by side.

    With these books and many others that I already have in my bookshelf, I hope to come up with a new conceptual definition of spin in physics.
  5. Mar 8, 2004 #4
    I have read chapter 1 of Kaku’s book. And as of 1992, the followings are the unresolved problems of GUTs (Grand Unified Theories). I am not aware whether some of these problems have been resolved by now (circa 2004) 12 years later.

    1. GUT cannot explain the three generations of particles.
    2. Higgs parameters (e.g. the mass) cannot be explained by a simpler principle.
    3. Scale for unification at the Planck’s domain must not exclude gravity from the theory.
    4. The existence of a “desert” region extending for 12 orders of magnitude from GUT scale down to scale of the electroweak.
    5. The “hierarchy problem,” caused by mixing the two energy scales together using radiative corrections will debunk the GUT program.

    The fifth problem is currently being studied under the research activities in the theory of supersymmetry.

    The conservation of H+ and H- in my independent research can make the assertion that proton decay will violate the compactification of H+ and H- at the Planck scale.

    Quarks are all compactified by the numerical series (Q-series) of 1, 3, 6, and multiple of 3, and 6.
    Leptons are all compactified by the numerical series (L-series) of 2, 4, 8 and its multiples.

    The 3-dimensional analog of the Q-series is the tetrahedron.
    The 3-dimensional analog of the L-series is the cube.

    It can be shown that for equal length of edges, the tetrahedron is more compact than the cube. The tetrahedron needs only four H’s at the least while the cube would need at least 8 H’s. Nature does not want to waste energy hence the tetrahedron is more stable than the cubic configuration.
  6. Mar 9, 2004 #5
    Traditionally, quantum field theory is the marriage of group theory and quantum mechanics.

    But a quantum field theory of mass such as the Higgs field must be the partnership of a modified ring theory and quantum mechanics.

    A ring theory is a more restrictive theory than group theory since it does not satisfy the existence of an inverse for each element of the set under the operation of multiplication. It is a semigroup.

    But what the ring theory makeup for its deficit in not having element-inverse is that its multiplicative operations are always commutative.

    The modified algebras of the ring is that of scalar factors that appear during the operations for addition and multiplication.

    This scalar factor becomes electric charge during addition and it becomes mass during multiplication.
  7. Mar 9, 2004 #6
    The disadvantage of a multiplicative set having no inverse is that its determinant is always zero and hence a metric cannot be defined.

    But the commutativity of a multiplicative set is a much deeper symmetry than a noncommutative multiplicative set. Nature will no doubt use a set containing more symmetry than one with lesser symmetry. The Higgs field must be using such a set.
  8. Mar 9, 2004 #7
    The following statement I made previously

    The disadvantage of a multiplicative set having no inverse is that its determinant is always zero and hence a metric cannot be defined.

    is false.

    According to matt grime (threader mathematician of the highest rank in my book) a 0-det matrix can still be able to possess a metric. These are not related properties and one can exist without the other.
  9. Mar 11, 2004 #8
    Pauli's spin matrices (excluding the identity matrix) are the following 2 by 2 matrices:

    \sigma_{1} = \left(\begin {array}{cc}0&1\\1&0\end{array}\right


    \sigma_{2} = \left(\begin {array}{cc}0&-i\\i&0\end{array}\right


    \sigma_{3} = \left(\begin {array}{cc}1&0\\0&-1\end{array}\right

    These are self-inverse matrices with determinants of -1. And whose even powers is the identity matrix and odd powers is itself.
  10. Mar 11, 2004 #9
    The pauli's matrices were derived from non-commutative relations.
    For commutative relations of H+ and H-, they can be expressed as the following:

    [tex]H^{+}=I - \sigma_{1}[/tex]


    [tex]H^{-}=\sigma_{1} - I[/tex]

    where I is the identity matrix.
  11. Mar 11, 2004 #10
    Dirac's 4 by 4 spin matrices are based on the Pauli's matrices.
    These don't have any analog in odd order of the matrix. But for the commutative H+ and H- group, both even and odd order exist.

    H+ and H- belong to a higher symmetry than the usual spin matrices of quantum mechanics. They actually can be used to describe the existence of double abstract spins in one-dimensional space leading to the concept of a double action integral.
  12. Mar 11, 2004 #11
    The existence of antimatter as proposed originally by Dirac took advantage of the two solutions from the quadratic form of energy.
    This anti-property is the existence of electric charge. Electron is different from positron only in the electric charge. One is negative and one is positive. Their masses are equal.

    The use of the quadratic form of energy in a double action integral can also give an anti-property for mass. These anti-property can be symbolized as H+ and H-. H+ is called the kinetic mass. H- is the potential mass. Only potential mass are affected by the force of gravity. Fermions have effective potential mass. So both masses of the electron and positron are potential mass. Bosons have effective kinetic mass. The photon does have kinetic mass in the form of E/c^2 but its potential mass is zero.

    The Higgs field is an equilibrium of H+ and H-. The masses of the W and Z bosons are kinetic masses, which are not affected by gravity.
    A Higgs boson is an H-. Although fermions are made of odd number of H+ and H-, while bosons are made of even number of H+ and H-, the entire universe is made of one big H-. The universe is neither a fermion nor a boson. For the universe to become a boson, it must interact with another H- universe of the same order. To become a fermion, it must interact with another H+ universe of the same order. The above implies that a Higgs particle can never be isolated as a fermion or as a boson by any physical experiment even at Planck scale of length, time, and energy.
  13. Mar 11, 2004 #12
    Does the universe have a net electric charge?

    All H+ and H- (regardless of their order) have an absolute value of electric charge of 1/6.

    If the H+ and H- are equal in number, the universe is static. There is no force.

    If there is a net of the number of H-, the universe is dynmaic. And all the four fundamental forces can exist.

    If there is a net of number of H+, the universe is still dynamic, but gravity would not exist globally and the universe will expand forever.
    This type of universe will definitely seek out another H- universe in order to interact with it to become a larger H- universe. In order to interact, these two universe must be of the same order.
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